Q: Apple iTouch5 Unexpected Power-Off

It's not called an "iTouch"

Try:                                               

- iOS: Not responding or does not turn on           

- Also try DFU mode after try recovery mode

How to put iPod touch / iPhone into DFU mode « Karthik's scribblings

- If not successful and you can't fully turn the iOS device fully off, let the battery fully drain. After charging for an least an hour try the above again.

- Try another cable              

- Try on another computer                                                       

- If still not successful that usually indicates a hardware problem and an appointment at the Genius Bar of an Apple store is in order.

Apple Retail Store - Genius Bar