randomly shuts off?

I just got my iphone5 (32gb) last week and today it randomly shut off and won't turn back on. My battery life was around 50% and when I went to check it, it wouldn't turn on. I've left it alone for a solid 2 hours and still hasn't turned on. Also, I've plugged it into the charger for about an hour and still hasn't turned on. any solutions to my problem?