Maybe it's a dead battery. You may need to buy a new one. Are you using an Apple charger and cable? What happens when you plug it in? How long do you leave it plugged in?
Apple batteries are designed to retain 80% capacity for 500 full charge cycles. Assuming you bought your 5c before it was discontinued you've had it for quite some time and the battery is showing its age. I agree with the previous responses and can tell you that it will only get worse, if it is indeed the battery.