Iphone 5 broken lock and home button?

A few months ago my lock button randomly stopped working. I don't recall doing anything to cause it to do so, i really did nothing about it because i could use assesive touch. But earlier in the week my home button completely fell out! I put it back in and it still works but it keeps falling out and sooner or later chances are i will lose it. I can still use assesive touch for this problem but it make things more difficult than they should be. So the question is, if i were to take my phone to an Apple store could they fix it? And what would the cost be? Or would it be free?

When did you get the iphone? If you answered under one year bring it back to the shop where you bought it. It will still be under warranty