Is it possible to define a template for a custom post type within a plugin independent of the active theme?

I’m writing a plugin to manage data about open-source projects. I developed an object model and have successfully created all custom post types and taxonomies, as well as implemented the correct capabilities/roles using the Members plugin. The appropriate users can create, modify, and delete their own posts, and administrators can approve them, as well as modify and delete anyone’s posts.

How to exclude latest x posts from a paginated query?

I have a WordPress loop, that is part of an AJAX call. Every time a button is clicked, this function is called, runs the below loop and outputs the next 6 posts. There are already five posts shown by default. How can I exclude the five latest (most recent published) posts from the WordPress loop? So that page 1 of the loop starts with the 6th, 7th, 8th, 9th, 10th & 11th post?