<?php

function getLastFiveCats() {

    global $wpdb;

    $query = "select t.term_id as term_ids, t.name, t.slug, max(p.ID) as id, tx.count from $wpdb->terms t, $wpdb->term_taxonomy tx, $wpdb->term_relationships tr, $wpdb->posts p where t.term_id = tx.term_id and tx.taxonomy = 'category' and tr.term_taxonomy_id = t.term_id and tr.object_id = id and p.post_status = 'publish' group by term_ids order by id desc limit 5";

    $results = $wpdb->get_results($query);

    foreach ($results as $result) {

        $catPermalink = get_bloginfo('url') . "/category/" . $result->slug . "/";

        ?>

            <li><a href='<?php echo $catPermalink ?>'><?php echo $result->name ?></a></li>

        <?php

    } 

}

?>