PROBLEM SOLVED!!!!
I was having the same issues with deplorable iPhone 5 battery life. The solution was posted earlier in this thread and it fixed my issues. The solution deals with restoring the iPhone 5 on iOS 6 as a new phone but it really works. My battery life is now better than my pervious iPhone 4.
I had my battery checked at the Apple store by a Genius and it checked out as normal. Whilst talking over the problems (and the aforementioned solution I saw on here) we decided to give it a go. The solution unfortunately involved setting the iPhone up as a new phone. YOU CAN STILL BACK UP CONTACTS AND OTHER IMPORTANT DATA.
1. Go to settings > iCloud > choose which individual items you want backed up.
NOTE: I didn't back up any apps because I don't use any to save data for. If you do - and you might want to confirm this with a Genius - go to Settings > iCloud > Storage & Backup > Manage Storage > Your Phone Name > then toggle apps on and off (again, not sure if this was even available when I originally backed up my iPhone and I didn't want to save anything from apps. I wanted a fresh install to fix the battery problem.)
2. Restore the iPhone at the Apple Store (to guarantee against a corrupt version of iOS 6).
3. Set the iPhone up as new. DO NOT click any of the options on the Apple Store computer. Disconnect from computer.
4. Restore backed up items from iCloud. (Genius will help you if its confusing - he had to help me 😉 )
5. Boom. You will have to tweak a few settings again and whatnot and probably set up email accounts again but trust me, its worth it. My battery is no longer an issue. My iPhone went to work with me yesterday charged to 100% and I used it off and on through the day on LGE with Facebook, apps, texting, phone calls, etc. And when I got home I continued using it til I went to sleep at 5am. I woke up today with over 50% battery remaining.
I'm not as eloquent as other folks on here but I really hope this helps.