Iphone 5 constant shutdown

For the past couple weeks my iphone has randomly shut down for no reason I can see. The battery will be high and it will still shut down every time I try to use it if it's not plugged to a charger. The diagnostic in settings files it as a low battery log crash even though batter says 100%. I'm not sure if this is the problem caused by ios 7 or because my battery has malfunctioned. Is anyone else having this problem or should I just get my battery or charger port replaced