My iPhone5 shuts off any time I take it out in cold weather when the battery is under 30%. Buy cold I mean like -5, 5 or 15 degrees F. Then when I plug it in, t

My iPhone5 shuts off any time I take it out in cold weather when the battery is under 30%. Buy cold I mean like -5, 5 or 15 degrees F. Then when I plug it in, the battery level immediately shows about 40%. Other than that and the low battery life in general, I'm pretty pleased with the phone.