diff --git a/wp-includes/admin-bar.php b/wp-includes/admin-bar.php
index c16ffc99a1..19d668c633 100644
--- a/wp-includes/admin-bar.php
+++ b/wp-includes/admin-bar.php
@@ -1117,8 +1117,9 @@ function wp_admin_bar_add_secondary_groups( $wp_admin_bar ) {
  * @since 3.1.0
  */
 function wp_admin_bar_header() {
+	$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/css"';
 	?>
-<style type="text/css" media="print">#wpadminbar { display:none; }</style>
+<style<?php echo $type_attr; ?> media="print">#wpadminbar { display:none; }</style>
 	<?php
 }
 
@@ -1128,9 +1129,9 @@ function wp_admin_bar_header() {
  * @since 3.1.0
  */
 function _admin_bar_bump_cb() {
-
+	$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/css"';
 	?>
-<style type="text/css" media="screen">
+<style<?php echo $type_attr; ?> media="screen">
 	html { margin-top: 32px !important; }
 	* html body { margin-top: 32px !important; }
 	@media screen and ( max-width: 782px ) {
diff --git a/wp-includes/class.wp-scripts.php b/wp-includes/class.wp-scripts.php
index 2df22b905a..2cda5a2990 100644
--- a/wp-includes/class.wp-scripts.php
+++ b/wp-includes/class.wp-scripts.php
@@ -122,6 +122,17 @@ class WP_Scripts extends WP_Dependencies {
 	 */
 	public $default_dirs;
 
+	/**
+	 * Holds a string which contains the type attribute for script tag.
+	 *
+	 * If the current theme does not declare HTML5 support for 'script',
+	 * then it initializes as `type='text/javascript'`.
+	 *
+	 * @since 5.3.0
+	 * @var string
+	 */
+	private $type_attr = '';
+
 	/**
 	 * Constructor.
 	 *
@@ -130,6 +141,10 @@ class WP_Scripts extends WP_Dependencies {
 	public function __construct() {
 		$this->init();
 		add_action( 'init', array( $this, 'init' ), 0 );
+
+		if ( ! current_theme_supports( 'html5', 'script' ) ) {
+			$this->type_attr = " type='text/javascript'";
+		}
 	}
 
 	/**
@@ -205,7 +220,7 @@ class WP_Scripts extends WP_Dependencies {
 			return $output;
 		}
 
-		echo "<script type='text/javascript'>\n"; // CDATA and type='text/javascript' is not needed for HTML 5.
+		echo "<script{$this->type_attr}>\n"; // CDATA and type="text/javascript" is not needed for HTML 5.
 		echo "/* <![CDATA[ */\n";
 		echo "$output\n";
 		echo "/* ]]> */\n";
@@ -266,15 +281,15 @@ class WP_Scripts extends WP_Dependencies {
 		$after_handle  = $this->print_inline_script( $handle, 'after', false );
 
 		if ( $before_handle ) {
-			$before_handle = sprintf( "<script type='text/javascript'>\n%s\n</script>\n", $before_handle );
+			$before_handle = sprintf( "<script%s>\n%s\n</script>\n", $this->type_attr, $before_handle );
 		}
 
 		if ( $after_handle ) {
-			$after_handle = sprintf( "<script type='text/javascript'>\n%s\n</script>\n", $after_handle );
+			$after_handle = sprintf( "<script%s>\n%s\n</script>\n", $this->type_attr, $after_handle );
 		}
 
 		if ( $before_handle || $after_handle ) {
-			$inline_script_tag = "{$cond_before}{$before_handle}{$after_handle}{$cond_after}";
+			$inline_script_tag = $cond_before . $before_handle . $after_handle . $cond_after;
 		} else {
 			$inline_script_tag = '';
 		}
@@ -334,7 +349,7 @@ class WP_Scripts extends WP_Dependencies {
 
 		$translations = $this->print_translations( $handle, false );
 		if ( $translations ) {
-			$translations = sprintf( "<script type='text/javascript'>\n%s\n</script>\n", $translations );
+			$translations = sprintf( "<script%s>\n%s\n</script>\n", $this->type_attr, $translations );
 		}
 
 		if ( ! preg_match( '|^(https?:)?//|', $src ) && ! ( $this->content_url && 0 === strpos( $src, $this->content_url ) ) ) {
@@ -352,7 +367,9 @@ class WP_Scripts extends WP_Dependencies {
 			return true;
 		}
 
-		$tag = "{$translations}{$cond_before}{$before_handle}<script type='text/javascript' src='$src'></script>\n{$after_handle}{$cond_after}";
+		$tag  = $translations . $cond_before . $before_handle;
+		$tag .= sprintf( "<script%s src='%s'></script>\n", $this->type_attr, $src );
+		$tag .= $after_handle . $cond_after;
 
 		/**
 		 * Filters the HTML script tag of an enqueued script.
@@ -422,7 +439,7 @@ class WP_Scripts extends WP_Dependencies {
 		$output = trim( implode( "\n", $output ), "\n" );
 
 		if ( $echo ) {
-			printf( "<script type='text/javascript'>\n%s\n</script>\n", $output );
+			printf( "<script%s>\n%s\n</script>\n", $this->type_attr, $output );
 		}
 
 		return $output;
@@ -557,7 +574,7 @@ class WP_Scripts extends WP_Dependencies {
 JS;
 
 		if ( $echo ) {
-			printf( "<script type='text/javascript'>\n%s\n</script>\n", $output );
+			printf( "<script%s>\n%s\n</script>\n", $this->type_attr, $output );
 		}
 
 		return $output;
diff --git a/wp-includes/class.wp-styles.php b/wp-includes/class.wp-styles.php
index 2d31717866..ebb9a596f0 100644
--- a/wp-includes/class.wp-styles.php
+++ b/wp-includes/class.wp-styles.php
@@ -100,6 +100,17 @@ class WP_Styles extends WP_Dependencies {
 	 */
 	public $default_dirs;
 
+	/**
+	 * Holds a string which contains the type attribute for style tag.
+	 *
+	 * If the current theme does not declare HTML5 support for 'style',
+	 * then it initializes as `type='text/css'`.
+	 *
+	 * @since 5.3.0
+	 * @var string
+	 */
+	private $type_attr = '';
+
 	/**
 	 * Constructor.
 	 *
@@ -114,6 +125,10 @@ class WP_Styles extends WP_Dependencies {
 		 * @param WP_Styles $this WP_Styles instance (passed by reference).
 		 */
 		do_action_ref_array( 'wp_default_styles', array( &$this ) );
+
+		if ( ! current_theme_supports( 'html5', 'style' ) ) {
+			$this->type_attr = " type='text/css'";
+		}
 	}
 
 	/**
@@ -156,7 +171,12 @@ class WP_Styles extends WP_Dependencies {
 		$inline_style = $this->print_inline_style( $handle, false );
 
 		if ( $inline_style ) {
-			$inline_style_tag = sprintf( "<style id='%s-inline-css' type='text/css'>\n%s\n</style>\n", esc_attr( $handle ), $inline_style );
+			$inline_style_tag = sprintf(
+				"<style id='%s-inline-css'%s>\n%s\n</style>\n",
+				esc_attr( $handle ),
+				$this->type_attr,
+				$inline_style
+			);
 		} else {
 			$inline_style_tag = '';
 		}
@@ -197,9 +217,17 @@ class WP_Styles extends WP_Dependencies {
 		}
 
 		$rel   = isset( $obj->extra['alt'] ) && $obj->extra['alt'] ? 'alternate stylesheet' : 'stylesheet';
-		$title = isset( $obj->extra['title'] ) ? "title='" . esc_attr( $obj->extra['title'] ) . "'" : '';
+		$title = isset( $obj->extra['title'] ) ? sprintf( "title='%s'", esc_attr( $obj->extra['title'] ) ) : '';
 
-		$tag = "<link rel='$rel' id='$handle-css' $title href='$href' type='text/css' media='$media' />\n";
+		$tag = sprintf(
+			"<link rel='%s' id='%s-css' %s href='%s'%s media='%s' />\n",
+			$rel,
+			$handle,
+			$title,
+			$href,
+			$this->type_attr,
+			$media
+		);
 
 		/**
 		 * Filters the HTML link tag of an enqueued style.
@@ -223,7 +251,16 @@ class WP_Styles extends WP_Dependencies {
 				$rtl_href = $this->_css_href( $obj->extra['rtl'], $ver, "$handle-rtl" );
 			}
 
-			$rtl_tag = "<link rel='$rel' id='$handle-rtl-css' $title href='$rtl_href' type='text/css' media='$media' />\n";
+			$rtl_tag = sprintf(
+				"<link rel='%s' id='%s-rtl-css' %s href='%s'%s media='%s' />\n",
+				$rel,
+				$handle,
+				$title,
+				$rtl_href,
+				$this->type_attr,
+				$media
+			);
+
 			/** This filter is documented in wp-includes/class.wp-styles.php */
 			$rtl_tag = apply_filters( 'style_loader_tag', $rtl_tag, $handle, $rtl_href, $media );
 
@@ -298,7 +335,12 @@ class WP_Styles extends WP_Dependencies {
 			return $output;
 		}
 
-		printf( "<style id='%s-inline-css' type='text/css'>\n%s\n</style>\n", esc_attr( $handle ), $output );
+		printf(
+			"<style id='%s-inline-css'%s>\n%s\n</style>\n",
+			esc_attr( $handle ),
+			$this->type_attr,
+			$output
+		);
 
 		return true;
 	}
diff --git a/wp-includes/embed.php b/wp-includes/embed.php
index c46b4b1cec..06e4472e44 100644
--- a/wp-includes/embed.php
+++ b/wp-includes/embed.php
@@ -1000,8 +1000,9 @@ function enqueue_embed_scripts() {
  * @since 4.4.0
  */
 function print_embed_styles() {
+	$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/css"';
 	?>
-	<style type="text/css">
+	<style<?php echo $type_attr; ?>>
 	<?php
 	if ( SCRIPT_DEBUG ) {
 		readfile( ABSPATH . WPINC . '/css/wp-embed-template.css' );
@@ -1032,8 +1033,9 @@ function print_embed_styles() {
  * @since 4.4.0
  */
 function print_embed_scripts() {
+	$type_attr = current_theme_supports( 'html5', 'script' ) ? '' : ' type="text/javascript"';
 	?>
-	<script type="text/javascript">
+	<script<?php echo $type_attr; ?>>
 	<?php
 	if ( SCRIPT_DEBUG ) {
 		readfile( ABSPATH . WPINC . '/js/wp-embed-template.js' );
diff --git a/wp-includes/formatting.php b/wp-includes/formatting.php
index b75bbaff3e..5d0ab841d3 100644
--- a/wp-includes/formatting.php
+++ b/wp-includes/formatting.php
@@ -5435,8 +5435,10 @@ function print_emoji_styles() {
 	}
 
 	$printed = true;
+
+	$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/css"';
 	?>
-<style type="text/css">
+<style<?php echo $type_attr; ?>>
 img.wp-smiley,
 img.emoji {
 	display: inline !important;
@@ -5517,7 +5519,8 @@ function _print_emoji_detection_script() {
 		'svgExt'  => apply_filters( 'emoji_svg_ext', '.svg' ),
 	);
 
-	$version = 'ver=' . get_bloginfo( 'version' );
+	$version   = 'ver=' . get_bloginfo( 'version' );
+	$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/javascript"';
 
 	if ( SCRIPT_DEBUG ) {
 		$settings['source'] = array(
@@ -5528,7 +5531,7 @@ function _print_emoji_detection_script() {
 		);
 
 		?>
-		<script type="text/javascript">
+		<script<?php echo $type_attr; ?>>
 			window._wpemojiSettings = <?php echo wp_json_encode( $settings ); ?>;
 			<?php readfile( ABSPATH . WPINC . '/js/wp-emoji-loader.js' ); ?>
 		</script>
@@ -5550,7 +5553,7 @@ function _print_emoji_detection_script() {
 		 * and edit wp-emoji-loader.js directly.
 		 */
 		?>
-		<script type="text/javascript">
+		<script<?php echo $type_attr; ?>>
 			window._wpemojiSettings = <?php echo wp_json_encode( $settings ); ?>;
 			!function(a,b,c){function d(a,b){var c=String.fromCharCode;l.clearRect(0,0,k.width,k.height),l.fillText(c.apply(this,a),0,0);var d=k.toDataURL();l.clearRect(0,0,k.width,k.height),l.fillText(c.apply(this,b),0,0);var e=k.toDataURL();return d===e}function e(a){var b;if(!l||!l.fillText)return!1;switch(l.textBaseline="top",l.font="600 32px Arial",a){case"flag":return!(b=d([127987,65039,8205,9895,65039],[127987,65039,8203,9895,65039]))&&(!(b=d([55356,56826,55356,56819],[55356,56826,8203,55356,56819]))&&(b=d([55356,57332,56128,56423,56128,56418,56128,56421,56128,56430,56128,56423,56128,56447],[55356,57332,8203,56128,56423,8203,56128,56418,8203,56128,56421,8203,56128,56430,8203,56128,56423,8203,56128,56447]),!b));case"emoji":return b=d([55357,56424,55356,57342,8205,55358,56605,8205,55357,56424,55356,57340],[55357,56424,55356,57342,8203,55358,56605,8203,55357,56424,55356,57340]),!b}return!1}function f(a){var c=b.createElement("script");c.src=a,c.defer=c.type="text/javascript",b.getElementsByTagName("head")[0].appendChild(c)}var g,h,i,j,k=b.createElement("canvas"),l=k.getContext&&k.getContext("2d");for(j=Array("flag","emoji"),c.supports={everything:!0,everythingExceptFlag:!0},i=0;i<j.length;i++)c.supports[j[i]]=e(j[i]),c.supports.everything=c.supports.everything&&c.supports[j[i]],"flag"!==j[i]&&(c.supports.everythingExceptFlag=c.supports.everythingExceptFlag&&c.supports[j[i]]);c.supports.everythingExceptFlag=c.supports.everythingExceptFlag&&!c.supports.flag,c.DOMReady=!1,c.readyCallback=function(){c.DOMReady=!0},c.supports.everything||(h=function(){c.readyCallback()},b.addEventListener?(b.addEventListener("DOMContentLoaded",h,!1),a.addEventListener("load",h,!1)):(a.attachEvent("onload",h),b.attachEvent("onreadystatechange",function(){"complete"===b.readyState&&c.readyCallback()})),g=c.source||{},g.concatemoji?f(g.concatemoji):g.wpemoji&&g.twemoji&&(f(g.twemoji),f(g.wpemoji)))}(window,document,window._wpemojiSettings);
 		</script>
diff --git a/wp-includes/media.php b/wp-includes/media.php
index 6a073ffd57..4117b78b37 100644
--- a/wp-includes/media.php
+++ b/wp-includes/media.php
@@ -1944,8 +1944,10 @@ function gallery_shortcode( $attr ) {
 	 *                    Otherwise, defaults to true.
 	 */
 	if ( apply_filters( 'use_default_gallery_style', ! $html5 ) ) {
+		$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/css"';
+
 		$gallery_style = "
-		<style type='text/css'>
+		<style{$type_attr}>
 			#{$selector} {
 				margin: auto;
 			}
diff --git a/wp-includes/script-loader.php b/wp-includes/script-loader.php
index eeb76639a7..52a8c44342 100644
--- a/wp-includes/script-loader.php
+++ b/wp-includes/script-loader.php
@@ -2465,11 +2465,12 @@ function _print_scripts() {
 		$zip = 'gzip';
 	}
 
-	$concat = trim( $wp_scripts->concat, ', ' );
+	$concat    = trim( $wp_scripts->concat, ', ' );
+	$type_attr = current_theme_supports( 'html5', 'script' ) ? '' : " type='text/javascript'";
 
 	if ( $concat ) {
 		if ( ! empty( $wp_scripts->print_code ) ) {
-			echo "\n<script type='text/javascript'>\n";
+			echo "\n<script{$type_attr}>\n";
 			echo "/* <![CDATA[ */\n"; // not needed in HTML 5
 			echo $wp_scripts->print_code;
 			echo "/* ]]> */\n";
@@ -2484,7 +2485,7 @@ function _print_scripts() {
 		}
 
 		$src = $wp_scripts->base_url . "/wp-admin/load-scripts.php?c={$zip}" . $concatenated . '&ver=' . $wp_scripts->default_version;
-		echo "<script type='text/javascript' src='" . esc_attr( $src ) . "'></script>\n";
+		echo "<script{$type_attr} src='" . esc_attr( $src ) . "'></script>\n";
 	}
 
 	if ( ! empty( $wp_scripts->print_html ) ) {
@@ -2646,7 +2647,8 @@ function _print_styles() {
 		$zip = 'gzip';
 	}
 
-	$concat = trim( $wp_styles->concat, ', ' );
+	$concat    = trim( $wp_styles->concat, ', ' );
+	$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/css"';
 
 	if ( $concat ) {
 		$dir = $wp_styles->text_direction;
@@ -2660,10 +2662,10 @@ function _print_styles() {
 		}
 
 		$href = $wp_styles->base_url . "/wp-admin/load-styles.php?c={$zip}&dir={$dir}" . $concatenated . '&ver=' . $ver;
-		echo "<link rel='stylesheet' href='" . esc_attr( $href ) . "' type='text/css' media='all' />\n";
+		echo "<link rel='stylesheet' href='" . esc_attr( $href ) . "'{$type_attr} media='all' />\n";
 
 		if ( ! empty( $wp_styles->print_code ) ) {
-			echo "<style type='text/css'>\n";
+			echo "<style{$type_attr}>\n";
 			echo $wp_styles->print_code;
 			echo "\n</style>\n";
 		}
diff --git a/wp-includes/theme.php b/wp-includes/theme.php
index 730ff902d6..e4cc8802f5 100644
--- a/wp-includes/theme.php
+++ b/wp-includes/theme.php
@@ -702,7 +702,14 @@ function locale_stylesheet() {
 	if ( empty( $stylesheet ) ) {
 		return;
 	}
-	echo '<link rel="stylesheet" href="' . $stylesheet . '" type="text/css" media="screen" />';
+
+	$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/css"';
+
+	printf(
+		'<link rel="stylesheet" href="%s"%s media="screen" />',
+		$stylesheet,
+		$type_attr
+	);
 }
 
 /**
@@ -1641,7 +1648,8 @@ function _custom_background_cb() {
 
 	if ( ! $background && ! $color ) {
 		if ( is_customize_preview() ) {
-			echo '<style type="text/css" id="custom-background-css"></style>';
+			$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/css"';
+			printf( '<style%s id="custom-background-css"></style>', $type_attr );
 		}
 		return;
 	}
@@ -1693,9 +1701,11 @@ function _custom_background_cb() {
 		$attachment = " background-attachment: $attachment;";
 
 		$style .= $image . $position . $size . $repeat . $attachment;
+
+		$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/css"';
 	}
 	?>
-<style type="text/css" id="custom-background-css">
+<style<?php echo $type_attr; ?> id="custom-background-css">
 body.custom-background { <?php echo trim( $style ); ?> }
 </style>
 	<?php
@@ -1709,8 +1719,9 @@ body.custom-background { <?php echo trim( $style ); ?> }
 function wp_custom_css_cb() {
 	$styles = wp_get_custom_css();
 	if ( $styles || is_customize_preview() ) :
+		$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/css"';
 		?>
-		<style type="text/css" id="wp-custom-css">
+		<style<?php echo $type_attr; ?> id="wp-custom-css">
 			<?php echo strip_tags( $styles ); // Note that esc_html() cannot be used because `div &gt; span` is not interpreted properly. ?>
 		</style>
 		<?php
@@ -2335,14 +2346,15 @@ function get_theme_starter_content() {
  *     ) );
  *
  * @since 2.9.0
- * @since 3.6.0 The `html5` feature was added
- * @since 3.9.0 The `html5` feature now also accepts 'gallery' and 'caption'
- * @since 4.1.0 The `title-tag` feature was added
- * @since 4.5.0 The `customize-selective-refresh-widgets` feature was added
- * @since 4.7.0 The `starter-content` feature was added
+ * @since 3.6.0 The `html5` feature was added.
+ * @since 3.9.0 The `html5` feature now also accepts 'gallery' and 'caption'.
+ * @since 4.1.0 The `title-tag` feature was added.
+ * @since 4.5.0 The `customize-selective-refresh-widgets` feature was added.
+ * @since 4.7.0 The `starter-content` feature was added.
  * @since 5.0.0 The `responsive-embeds`, `align-wide`, `dark-editor-style`, `disable-custom-colors`,
  *              `disable-custom-font-sizes`, `editor-color-palette`, `editor-font-sizes`,
  *              `editor-styles`, and `wp-block-styles` features were added.
+ * @since 5.3.0 The `html5` feature now also accepts 'script' and 'style'.
  *
  * @global array $_wp_theme_features
  *
@@ -2635,9 +2647,10 @@ function _custom_logo_header_styles() {
 		$classes = array_map( 'sanitize_html_class', $classes );
 		$classes = '.' . implode( ', .', $classes );
 
+		$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/css"';
 		?>
 		<!-- Custom Logo: hide header text -->
-		<style id="custom-logo-css" type="text/css">
+		<style id="custom-logo-css"<?php echo $type_attr; ?>>
 			<?php echo $classes; ?> {
 				position: absolute;
 				clip: rect(1px, 1px, 1px, 1px);
@@ -3196,15 +3209,15 @@ function wp_customize_support_script() {
 	$admin_origin = parse_url( admin_url() );
 	$home_origin  = parse_url( home_url() );
 	$cross_domain = ( strtolower( $admin_origin['host'] ) != strtolower( $home_origin['host'] ) );
-
+	$type_attr    = current_theme_supports( 'html5', 'script' ) ? '' : ' type="text/javascript"';
 	?>
 	<!--[if lte IE 8]>
-		<script type="text/javascript">
+		<script<?php echo $type_attr; ?>>
 			document.body.className = document.body.className.replace( /(^|\s)(no-)?customize-support(?=\s|$)/, '' ) + ' no-customize-support';
 		</script>
 	<![endif]-->
 	<!--[if gte IE 9]><!-->
-		<script type="text/javascript">
+		<script<?php echo $type_attr; ?>>
 			(function() {
 				var request, b = document.body, c = 'className', cs = 'customize-support', rcs = new RegExp('(^|\\s+)(no-)?'+cs+'(\\s+|$)');
 
diff --git a/wp-includes/version.php b/wp-includes/version.php
index 8f9320d427..cb53fb749d 100644
--- a/wp-includes/version.php
+++ b/wp-includes/version.php
@@ -13,7 +13,7 @@
  *
  * @global string $wp_version
  */
-$wp_version = '5.3-alpha-46163';
+$wp_version = '5.3-alpha-46164';
 
 /**
  * Holds the WordPress DB revision, increments when changes are made to the WordPress DB schema.
diff --git a/wp-includes/widgets/class-wp-widget-archives.php b/wp-includes/widgets/class-wp-widget-archives.php
index db3a91d654..4cf0db82c9 100644
--- a/wp-includes/widgets/class-wp-widget-archives.php
+++ b/wp-includes/widgets/class-wp-widget-archives.php
@@ -98,6 +98,8 @@ class WP_Widget_Archives extends WP_Widget {
 					$label = __( 'Select Post' );
 					break;
 			}
+
+			$type_attr = current_theme_supports( 'html5', 'script' ) ? '' : ' type="text/javascript"';
 			?>
 
 			<option value=""><?php echo esc_attr( $label ); ?></option>
@@ -105,7 +107,7 @@ class WP_Widget_Archives extends WP_Widget {
 
 		</select>
 
-<script type='text/javascript'>
+<script<?php echo $type_attr; ?>>
 /* <![CDATA[ */
 (function() {
 	var dropdown = document.getElementById( "<?php echo esc_js( $dropdown_id ); ?>" );
diff --git a/wp-includes/widgets/class-wp-widget-categories.php b/wp-includes/widgets/class-wp-widget-categories.php
index 780993e3d9..92f30c0a85 100644
--- a/wp-includes/widgets/class-wp-widget-categories.php
+++ b/wp-includes/widgets/class-wp-widget-categories.php
@@ -89,9 +89,11 @@ class WP_Widget_Categories extends WP_Widget {
 			wp_dropdown_categories( apply_filters( 'widget_categories_dropdown_args', $cat_args, $instance ) );
 
 			echo '</form>';
+
+			$type_attr = current_theme_supports( 'html5', 'script' ) ? '' : ' type="text/javascript"';
 			?>
 
-<script type='text/javascript'>
+<script<?php echo $type_attr; ?>>
 /* <![CDATA[ */
 (function() {
 	var dropdown = document.getElementById( "<?php echo esc_js( $dropdown_id ); ?>" );
diff --git a/wp-includes/widgets/class-wp-widget-recent-comments.php b/wp-includes/widgets/class-wp-widget-recent-comments.php
index 6d9ce47604..6d89eeea24 100644
--- a/wp-includes/widgets/class-wp-widget-recent-comments.php
+++ b/wp-includes/widgets/class-wp-widget-recent-comments.php
@@ -53,9 +53,13 @@ class WP_Widget_Recent_Comments extends WP_Widget {
 			|| ! apply_filters( 'show_recent_comments_widget_style', true, $this->id_base ) ) {
 			return;
 		}
-		?>
-		<style type="text/css">.recentcomments a{display:inline !important;padding:0 !important;margin:0 !important;}</style>
-		<?php
+
+		$type_attr = current_theme_supports( 'html5', 'style' ) ? '' : ' type="text/css"';
+
+		printf(
+			'<style%s>.recentcomments a{display:inline !important;padding:0 !important;margin:0 !important;}</style>',
+			$type_attr
+		);
 	}
 
 	/**