IPhone 5 won't turn on or restore?

I have had an iPhone 5 since Christmas now, and everything was fine. Recently the phone started turning itself off, fading to black before restarting itself. This has just happened and now the phone loads the apple logo for around 2 seconds and then fades and repeats the process. Even plugging the phone into my laptop does not help. As soon as it starts to turn on it fades and reboots. I have tried putting the phone into recovery mode and that still does not work. Any advice would be awesome. The phone is in warranty but the Apple store is a fair while away for me to travel to.

Battery / power problem. Best to send it in mate.

As your phone is in warranty period, so its better contact apple care to resolve this problem permanently.

Apple knows the most, contact or visit the apple store As soon as possible.

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