See
hereAffects some iPhones bought between September 2012 and January 2013. Just type in your serial number and you'll find out if you're eligible for a free battery replacement from Apple.
Typically, mine is one of the limited batch with the problem, with no authorised/recognised store in my area to replace it
Nearest one is about an hour away from me, so, is it worth it?
Other option would be to get it done at the Bullring while in the area for the Clubs Agm (would be about 30 mins or so away from the hotel I'll be at).
Thought it was worth posting the info up on here though for anyone else who has an iPhone 5