IPhone 5 shutting off randomly?

My iPhone 5 keeps shutting off all the way by itself. When I'm using it after a couple minutes it will just completely turn off or even when its in my pocket it will shut down. I backed everything up and am attempting to restore it, but it can't even stay on long enough to complete the restore as it shuts down just like before. Battery life is fine, it's not jailbroken or anything.

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Plug it into iTunes and restore it from there. If that doesn't work, go to your nearest Apple Store and they will replace it. Since you have a iPhone 5, and it hasn't been out for a year yet, you are still under warranty with Apple.

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