If my iPhone 5s was to break the lock/home button. What do I do?

I have insurance on my phone with AT&T. But would that cover me if my phone's lock/home button were to break?

Well if the home button stops working AT&T coverage would take care of it. Also if still under warranty through Apple they would service/replace it for free. I would also advise getting Applecare through Apple.

Apple would be the better people to get ahold of since AT&T has terrible customer service.