I thought this thread might be of use to some Iphone 5 users. I have just had the battery in my two year old Iphone 5 replaced free of charge at an Apple Store .
Apple have admitted that a number of IPhone 5 mobile phones were fitted with faulty batteries and have set up a battery replacement program. The faulty batteries were fitted to phones produced within a five month window from September 2012 to January 2013.... Apple have not exactly done a good job of publicising this fact in the Uk though!
The fault means that the battery does not last as long as it should. I have never been happy with my phones battery performance since the phone was new, I recently found out about this problem by accident whilst googling iPhone 5 battery problems, you can either enter your serial number or IMEI number online, ring the Apple technical support number or take your Iphone5 into an Apple Store to tell if your phone is affected and therefore qualifies for a new battery, free of charge.
If your phone qualifies then you make an appointment with your nearest Apple Store to replace the battery for you, you can then normally collect your phone about 90 minutes later.
It is advisable to back up your phones data firstly with something like Icloud. This is already on your phone, it offers a free back up service for data up to 5 GB or you can pay 79p a month which gives you up to 20GB. (I had to do this). This will depend on how much data/ photos etc you have on your iPhone. You can if you wish just pay for 1 months extra use if needed and then go back to the free 5 GB of storage.... You just go into settings on your phone and down to iCloud and then back up... It is straight forward from there.
Incidently the battery would otherwise cost about £60 to get replaced at an Apple Store.... It can also be sent off, though there is about a 5 day turn around to get your phone back.
I Hope this helps.