Q: iPhone 5 restarting problem

My iPhone 5 keeps shutting off and sometimes will restart itself. Before shutting off the screen will get lines or turn colours. Sometimes when restarting it only makes it as far as to show the Apple Logo, then will try to reboot again. I have tried restoring the phone through iTunes, seems to work for longer, then approx 20 minutes later, it will shut off again. Sometimes it won't turn on right away and sometimes it will. Usually to get it to turn on I have to hold in the lock & home button, occasionally it will turn on with just the lock button. Just wondering if anyone knows if this could be something loose in the phone? Or is it my screen or battery? Or could it possibly mean that the hard drive in my phone has gone bad? Please help!