I had a problem with weak battery as well. I even wrote to Phil Schiller about it (including a real story where the weak battery on iPhone 5 nearly left me stranded in the middle of the night because I called a cab literally with 1 % left). My iPhone 5 got only 4 hours on battery without any battery-heavy apps.
Apple PR person together with some high-level technical support from United States (which supposedly is not available to regular customers and it was only because of the request from Schiller) diagnosed my battery logs and after nearly two weeks of logging and calls from Apple they stated that according to logs, there is no problem with the battery.
I tried everything, restoring, DFU, setting iPhone as new, nothing helped.
Suddenly after a week or so, my battery is getting better and better. Currently it gets 5:30 of usage (one and half hour more than usual). So I suspect that either the predictive part of iOS 7 kicked in, or some app caused the battery drain and was updated. This might also explain that some people are having battery problems and some don't.