My iPhone turns off while charging

I plugged my iPhone 5S into charge after is had ran out of battery. It turned back on and I was watching a video when it dies again and turns off. I press the lock button and all I see is the battery charging icon after the phone has died and is put on to charge. It stays on that screen for over 5 mins before turning on again. It is really starting to annoy me and I want to know if theres any way of fixi.

Thanks