There’s Help Available For Your iPhone 5 Battery
If you bought one of the early iPhone 5 models you may have noticed that you have to recharge more often than you'd like. According to ARS Technica, Apple has just announced a new program to solve your problem. Apple will replace your battery if you bought your phone between September of 2012 and January of 2013. To see if your phone is eligible visit the Apple website by clicking here.
You can find your serial number in Settings under About. If your phone qualifies Apple urges you back up your phone either to your computer or iCloud, turn off Find My Phone and reset the phone to it's factory default settings.
To get your battery changed you will have to bring your phone to Apple service provider, an Apple Retail Store, or make arrangements with Apple's phone support technicians.
This program will be effective until March 1, 2015 or two years from the date of purchase.