Get latest posts from multiple categories

2 choices here, you either need to set the category as an array e.g.

$args = array( 
 'posts_per_page' => 5,
 'category' => array(15,16,17,18,19)
);

You can’t just add the numbers in a list but I can’t find any documentation that the category element allows multiples (as the name is category)

The other option is to use wp_query and category__in

$query = new WP_Query(
 array(
  'category__in' => array(15,16,17,18,19),
  'posts_per_page' => 5,
  'post_type' => 'post',
 )
 );
if ( $query->have_posts() ) {
 while ( $query->have_posts() ) {
  $query->the_post();
  // do something
 }
}
wp_reset_postdata();

These will get the 5 last posts from any of those categories, if you want to get a post from each of them then the query needs to be a lot different