My iPhone won't make it past the apple logo when turning on!

Okay, I have a problem with my iPhone 5. It all started yesterday when I wasn't using my phone it would shut off (even though it was charged.) Everytime I rebooted it it would go to the homescreen and shut off. Not thinking anything of it I plugged my phone in. Since then, when it's on the charger it begins to turn itself on but doesn't make it past the apple logo screen then it goes black. (And it continues to do this when it's on the charger.) When not on the charger it won't even begin to turn on. Please help! What should I do?