Apple has released the following statement via their support channel:
"Apple has recently discovered that a certain number of iPhone 5 batteries have not performed like they had expected, either due to shorter battery life or just for the lack of holding a charge. If you purchased your iPhone between the dates of September 2012 and January 2013 your iPhone may qualify for a free replacement."
How do I know if my iPhone qualifies?
Head on over to this website: https://ssl.apple.com/support/iphone5-battery/. It has all the information you need to know as well as a place for you to put in your phone’s serial number to check your eligibility.
What do I do if my iPhone is eligible?
There are a few options that you can choose from in order to get your battery replaced if your iPhone qualifies. You can sign up for an appointment and go to your nearest Apple Store, Go to an Apple authorized dealer like us (CityMac) or you can contact Apple support at their number here (1-800-275-2273) and they can direct you to the best options for you.
What should I do before I get my iPhone repaired?
It is always best to back up your iPhone data and you can do this either through an iCloud backup in your iPhones settings or by backing up your iPhone to your computer through iTunes.
If my screen is cracked will I still be eligible for the program?
Unfortunately if your screen is cracked it will not be eligible for replacement until after it is replaced. In order to replace the battery, the screen must be taken off and if the screen is cracked it would impede the ability to replace the battery without further damaging the phone.