My iphone 5 won't go past the apple logo?

It just shuts off after like a min of hanging on the apple logo.

Added (1). I've tried all the button combinations and itunes for restore

Try pressing the power button and the home button at the same time.

Try this:

Hold both the home and power buttons at the same time. When the Apple boot logo appears, let go of the power button but continue holding the home button.

If a restore didn't work then something is wrong with one of the components. A restore will fix any software related problem apart from bugs that is in the operating system. The iPhone being stuck on the boot screen can be many different hardware problems. You're best to go to an Apple Store and they can do a diagnostic test to find out what is causing the problem.

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