I have the same problem man.
Iphone 5 16g black
Keeps restarting itself every 2-5 minutes.
I restored it, did not back it up and start as new phone. Problem still occuring.
The typing on the phone seems too glichy as well as scrolling on the screen
Right before the iPhone restarts itself, wavy lines appear and shuts off and reboots.
Battery fully charged, however the percentage is off. (when charging the % gets stuck at random, not giving accurate reading.)
As I typed this my iPhone 5 has restarted itself 3 times.
Apple, please help us out fast. I dont want to drive to the apple store thats 50 miles away either. Thanks!