There's an app on the phone that is stuck sending data, or trying to send and failing, and in an infinite loop. Mail can do this if you have an Exchange account or iCloud account. Sometimes a corrupt calendar entry or contact can cause this.
But first, if you have either type of account go into Settings and turn it off, then reboot the phone (hold HOME and SLEEP until an Apple logo appears). If the problem goes away you have identified the culprit. If you turn the account back on and the problem does not come back no further action is required.
If this doesn't fix it you have to find the app. Any app that exchanges a lot of data (Facebook, Whatsapp, etc) is a possibility.
I have been using my Iphone 5 for about two weeks now. The battery life seems to be a major issue. I have tried resetting, setting up as a new iphone. When my phone is on Airplane mode the battery is fantastic but when i turn my mobile service back on it lasts about 4~5 hours only. I have tried all the battery saving tips aswell.