My Iphone that has never been jailbroken is stuck in a boot loop and when i try to restore it in or out of recoverymode it loses conection to itunes. how do i fix it?

When I plug my iPhone 5 into the wall or my computer it starts a boot loop between the charging but not on screen, the apple logo/power up screen, and then it turns off, and repeats, or when I put it into recovery mode it also disconnects right after iTunes finishes extracting the software. I have never had anything replaced in the iPhone nor have I ever Jailbroken my iPhone.