function get_most_recent_categories($limit = 5) {
    // retrieve all categories
    $categories = get_categories();
    $recent_posts = array();
    foreach ($categories as $key=>$category) {
        // get latest post from $category
        $args = array(
            'numberposts' => 1,
            'category' => $category->term_id,
        );
        $post = get_posts($args)[0];
        // save category id & post date in an array
        $recent_posts[ $category->term_id ] = strtotime($post->post_date);
    }

    // order by post date, preserve category_id
    arsort($recent_posts);

    // get $limit most recent category ids
    $recent_categories = array_slice(array_keys($recent_posts), 0, $limit);

    return $recent_categories;
}