Sort categories by latest post published

I’ve seen this here on the forums and with a few changes I’ve got the following setup:

<?php
  $cat_args = array('orderby' => 'name',
                    'order' => 'ASC');
  $categories = get_categories($cat_args);
  foreach($categories as $category) {
    $args = array('posts_per_page' => 5,
                  'category__in' => array($category->term_id),
                  'ignore_sticky_posts' => true );
    $posts = get_posts($args);
    if ($posts) {
      foreach($posts as $post) {
        setup_postdata($post);
        /* Post Loop */
      }
    }
  }
?>

The thing is that I need the categories to be ordered by the latest post published. E.g. if new post is published in a category “abc” which is in position 7 it will be moved to position 1 and push all other categories down one.

Does anybody have any idea how this could be done?