// add ie conditional html5 shim to header

functions.php

<?php
// add ie conditional html5 shim to header
function _s_add_ie_html5_shim () {
    echo '<!--[if lt IE 9]>';
    echo '<script src="' . get_template_directory_uri() . '/js/html5.js"></script>';
    echo '<![endif]-->';
}
add_action('wp_head', '_s_add_ie_html5_shim');

wp-4.1-functions.php

<?php
/**
 * Enqueue scripts and styles.
 */
function _s_scripts() {
	wp_enqueue_script( '_s-html5shiv', get_template_directory_uri() . '/js/html5shiv.js', array(), '3.7.2', false );
}
add_action( 'wp_enqueue_scripts', '_s_scripts' );

/**
 * Load only in IE as of WP 4.1
 */
function _s_html5shiv( $tag, $handle, $src ) {
	if ( '_s-html5shiv' === $handle ) {
		$tag = "<!--[if lt IE 9]>\n" . $tag . "<![endif]-->\n";
	}
	return $tag;
}
add_filter( 'script_loader_tag', '_s_html5shiv', 10, 3 );

wp-4.2-functions.php

<?php
/**
 * Enqueue scripts and styles.
 */
function _s_scripts() {
	wp_enqueue_script( '_s-html5shiv', get_template_directory_uri() . '/js/html5shiv.js', array(), '3.7.2', false );
	wp_script_add_data( '_s-html5shiv', 'conditional', 'lt IE 9' );
}
add_action( 'wp_enqueue_scripts', '_s_scripts' );

@bryanwillis Thanks I did not know about the function wp_script_add_data()

I am not sure why a caching plugin would break this as the code is just generating HTML code which will be present on every page.