exclude cat redux

I’ve got a page on one of my sites that should only show certain posts from certain categories. I’ve gotten as far as creating my loop but I think I’m doing something wrong. With this loop it shows only children of cat 5 but it’s not excluding cat 13. It is excluding cat 16. Anyone able to tell me what I’m doing wrong? Thanks in advance! Code to follow.

-A

<?php  $cats = get_categories('orderby=id&order=DESC&child_of=5&$category->cat_ID>16&exclude=13&exclude=16');
		// This is a loop that pulls any special categories

			foreach ($cats as $cat) :
				echo '<h1>' . $cat->name . '</h1>';
				query_posts( 'orderby=date&order=ASC&cat='.$cat->term_id );
				    if (have_posts()) : while (have_posts()) : the_post(); ?>
					<?php the_content(); ?>
				    <?php endwhile; endif; wp_reset_query(); ?>

			<?php endforeach; ?>