iPod touch 5 will not start after I shut down last night.

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

I tried a community solve. Press the power button on top edge, and reset button on the bottom face, for 20 seconds. The apple logo will appear and the machine will function normally.