WordPress MU

Scenario:
On my blog homepage I make a call to the loop at the bottom of the page. The user sees 5 articles, and below that they can click on 'older articles' to see prior articles.

url would be like mysite.com/page/2/

How do I apply a different template to the 2,3,4 etc.. pages?

I really need to change it as I have sliders and galleries among other things on my index page. There is absolutely no reason to be showing that information on 'older articles'...

I have my own page.php and archive.php files in my theme, but obviously they are not called in the wp architecture for 'more' pages.

What do I need to name a custom template to work in this area? (index-page*.php) etc.

And no, I do not have the option of assigning a 'custom homepage' template instead of the index, as I am going to use that page as a splash intro for the site.

I can't imagine that wp has not thought about templating 'older articles' loops from the index file.

Take a look at the template heirarchy information:
http://codex.wordpress.org/Template_Hierarchy

Make all your mods to home.php instead of index.php. Home.php will by your "home page" and index.php will handle all the rest of the loops.

I am already using home.php for a splash intro page otherwise your idea would work perfectly.

From what I can see in the Hierarchy it looks like wp does not have an 'index2.php' or any type of architecture beyond home/index/category/single

Is there a way to 'hack' in another step to the hierarchy of wp?

Okay, I misunderstood. What you want to do is apply a custom template to just the "special" page - "page 2." So, you make a special template in your theme like it says to do here:
http://codex.wordpress.org/Pages#Creating_Your_Own_Page_Templates

Then, for your page 2, apply the special template, and let all the other pages run through the normal index.php.