My iphone 5 keeps rebooting after software update

April 2013. Just updated software on iphone 5 to ios 6.1.3. Since then the phone is restarting/rebooting every 2-3 minutes? Sometimes the screen quickly goes to a pinstripe and then cuts out. 10 seconds later the phone give me the apple logo and restarts quuickly. Can't get the phone to stay on long enough to back up. I suppose I'll need to reset. I also seem to be getting conflicting battery life readings even after charging over night,

Anyonw else having this issue?

Thanks