First setup a WP_Query to fetch the latest 5 posts from your custom post type “apps”. You also need to update a “counter” for each post in the loop. Then simply echo the count in the class for the div.
<?php
//Query posts
$query = new WP_Query(array(
'post_type' => 'apps',
'posts_per_page' => 5
));
//Reset counter
$count = 0;
?>
<?php if ($query->have_posts()) : ?>
<div id="header">
<?php while ($query->have_posts()) : $query->the_post(); ?>
<?php $count++; //update count ?>
<div class="post_<?php echo $count; //prints the class as "post_XX" ?>">
<?php if( has_post_thumbnail() ) { the_post_thumbnail(); } ?>
</div>
<?php endwhile; ?>
</div>
<?php endif; ?>
<?php wp_reset_query(); ?>
This should return the results as
<div class="post_1"><img src="https://wordpress.stackexchange.com/questions/72405/.." /></div>
<div class="post_2"><img src="https://wordpress.stackexchange.com/questions/72405/.." /></div>
<div class="post_3"><img src="https://wordpress.stackexchange.com/questions/72405/.." /></div>
<div class="post_4"><img src="https://wordpress.stackexchange.com/questions/72405/.." /></div>
<div class="post_5"><img src="https://wordpress.stackexchange.com/questions/72405/.." /></div>