This is how I did it. If you have your custom post type as “projects”, and your category as “airplane”.
If you’re not planning on using the pre-build loop you would make another one called loop-projects.php. However, it’s not necessary.
<?php
$args = array(
'numberposts' => 5,
'post_type' => 'projects',
'category_name' => 'airplane');
query_posts( $args );
get_template_part( 'loop', 'projects' );
wp_reset_query();
?>