Loop and display most recent post from multiple categories

I’ve seen responses for this, but they either don’t function properly or don’t quite answer my question.

I’m trying to use a loop to create slides for a slideshow. Each slide shows the most recent post from 5 different categories. The below code works, except that it’s showing the 5 most recent posts from all categories and not each category. ie., it shows 2 posts from category 7 and the 4 following most recent categories.

My guess is that a foreach statement should work, but I keep getting stuck. Help!

<?php
$cat_post_query = new WP_Query($query_string . 'cat=7,8,10,9,11');
while ($cat_post_query->have_posts()) : $cat_post_query->the_post();
$do_not_duplicate = $post->ID;?>

<div>
* post content*
</div>

<?php endwhile;  ?>