My iPhone 5 battery
My iPhone 5 shuts off when it reaches 5%. It never used to do that before. Any suggestions?
iPhone 5, iOS 6
What I recommend is a clean restore using iTunes. A backup is required just so your iPhone isn't erased.
iTunes: Restoring iOS software
http://support.apple.com/kb/HT1414
iOS: How to back up
http://support.apple.com/kb/HT1766
If the problem still happens, you need to setup your iPhone as a new device.
iOS: How to back up your data and set up as a new device
http://support.apple.com/kb/HT4137
One of these don't solve your issue, you may need to get service from Apple.