Apple have (suddenly) realised that a (small) number of iPhone 5 users have severe battery problems (I.e. The battery life is too short). So Apple is going to replace them free
https://ssl.apple.com/uk/support/iphone5-battery/
Mine is on the list
Replacement program begins on 29/8/14
https://ssl.apple.com/uk/support/iphone5-battery/
Mine is on the list
Replacement program begins on 29/8/14