Why does my iPhone 5 keep turning off every 5 minutes?

After using the 'personal hotspot' feature yesterday, my iPhone 5 has been acting up. I'm not sure whether the personal hotspot caused this? But this is the only different thing that has occured on my iphone, after around 4-5 hours of using the hotspot, my phone stopped charging, it said it was fully charged, but really it was about 18%. I reset this and it was fine. About an hour later, it started turning off every 5 minutes when the screen was asleep, i have reset it a further 4 times, and for around 2-3 hours it's like a normal iphone, but then starts shutting off again every 5 minutes. When the screen is on, it never shuts off, only when the screen is sleeping.

Anyone got any ideas?

Greatly appreciated, thanks