How to use add_theme_support(‘html5’)?

According to the documentation, you must pass an array of items where you want to enable HTML5 markup:

add_theme_support( 'html5', array(
    // Any or all of these.
    'comment-list', 
    'comment-form',
    'search-form',
    'gallery',
    'caption',
) );

The documentation also recommends using add_theme_support() on the after_setup_theme hook, stating that the init hook may be too late for some features.

Reference

Developer documentation: add_theme_support() » HTML5