iPhone 5 keep resetting

My iPhone 5 started glitching out and restarting until finally it would not turn on. So I plugged it in and I was able to get about 10 more minutes out of it in which I reset my phone and restored it. But now it won't even turn on when plugged in. It just keeps showing the apple start up logo and then shutting off before it could finish booting up. I didn't drop it, get water on it, jailbreak it, or anything else! What can I do?