fe-modify-num-of-posts-per-page-on-fe-recipe.php

<?php
/**
 * Set the number of posts on the Custom Post Type archive for `fe_recipe` to 5.
 */

add_action( 'pre_get_posts', 'fe_modify_number_of_posts_per_page' );

/**
 * Modify Posts Per Page for CPT `fe_recipe`
 *
 * @param WP_Query $query The current query about to be run.
 */
function fe_modify_number_of_posts_per_page( $query ) {

	if ( ! $query->is_main_query() ) {
		return;
	}

	if (
		isset( $query->query['post_type'] )
		&& 'fe_recipe' === $query->query['post_type']
	) {
		$query->set( 'posts_per_page', 5 );
	}

}