Apple has started an iPhone 5 Battery Replacement Program. It is for some iPhone 5 devices sold between September 2012 and January 2013 that are experiencing shorter than normal battery life. This program will replace qualified batteries free of charge, even if the iPhone is out of warranty.

To determine of your iPhone 5 qualifies for this program, find it’s serial number by going to Settings->General->About, and enter it here: https://ssl.apple.com/support/iphone5-battery