IPhone 5s :: Keeps Rebooting Itself Every 2 Seconds

My phone died last night like it usually happens after a long day of usage and I thought nothing of it until I got home and tried charging it. After it came back on (apple logo came on the screen) it kept vibrating signaling that it was charging every two seconds, the screen then would go black and the apple logo would come back and the vibration indicating it was charging would come back on. There was one or two times when my lock screen would show up for a second or so but then it would go black and restart itself over and over and over and over again. I cant even get the lock screen to stay on the phone for longer than a second or two and it restarts itself again.

So I then thought of plugging it into my computer to see what would happen and maybe even restoring it from a back up but it would not let me because I have to turn off find my iPhone... which I can't because I cant get it to stay on for longer than a **** second. iTunes does recognize my phone though and so does iPhoto but that's all I can do! I'm trying to let the phone COMPLETELY die as in it won't even notify me that it needs to be charged to see if that makes a difference but I have no clue what's going on nor why this is happening to me or what the solution is! I've tried holding down the home/power buttons but while it has battery all it does is keep restarting and while its dead it just tells me to plug it into a charger