Show one same template for two category

You can do it in many ways.

Two solutions I recommend are:

1. Editing category template

Just edit your category.php template and put if statement in there:

if ( is_category( array(15, 19) ) )
  get_template_part('category-15-19');
else
  get_template_part('category-all')

Then just put code for category 15 and 19 into category-15-19.php file and code for other categories into category-all.php file.

2. Using template_include hook

Add filter to template_include hook. It should return template name that should be displayed by WordPress.

function my_categories_template($template_name) {
   if ( is_category( array(15, 19) ) )
       return 'category-15-19.php';
   return $template_name;
}
add_filter( 'template_include', 'my_categories_template' );