get_posts no older than X days - Wordpress

As of 3.7 you can use date_query https://developer.wordpress.org/reference/classes/wp_query/#date-parameters

So it would look like:

$args = array(
    'posts_per_page' => 5,
    'post_type' => 'post',
    'orderby' => 'comment_count',
    'order' => 'DESC',
    'date_query' => array(
        'after' => date('Y-m-d', strtotime('-10 days')) 
    )
); 
$posts = get_posts($args);

The exemple from the doc should work just fine. get_posts() uses WP_Query() behind the scene to make the actual request. For your case the modified example should look something like this:

// Create a new filtering function that will add our where clause to the query
function filter_where( $where = '' ) {
    // posts in the last 30 days
    $where .= " AND post_date > '" . date('Y-m-d', strtotime('-10 days')) . "'";
    return $where;
}

add_filter( 'posts_where', 'filter_where' );
$query = get_posts(array (
            'numberposts' => 5,
            'orderby'=>'comment_count',
            'order'=>'DESC',
            'post_type'   => array ( 'post' )
         ));
remove_filter( 'posts_where', 'filter_where' );