iPhone 5 randomly turns off

I went to bed with 35% battery,

I woke 7 hrs later to a txt message tone, but upon grabbing my phone to look at it, it appeared the battery had just died!

I pressed the home key, the power switch but nothing.

As such I grabbed my laptop and plugged it in to give it some power only then for the apple logo to instantly appear on screen. It then indicated I had approx 17% power left. Weird. I left it plugged in regardless.

5 mins later I came back, pressed the home screen key again, nothing, pressed the power button, nothing. Pulled the USB cable out and put it back in.....

Low and behold the apple logo reappeared and 15-20 seconds later I could use the phone!

I have an iPhone 5

Model: MD662B/A

iOS: 7.0.4(11B554a)

Anyone else experienced this or have ideas why this happens?

Thanks,

Ant