Q: My ipod touch 5th gen won't restore

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                                     

And maybe:

Update Server

Try:

- Powering off and then back on your router.

- iTunes for Windows: iTunes cannot contact the iPhone, iPad, or iPod software update server

- Change the DNS to either Google's or Open DNS servers

Public DNS — Google Developers

OpenDNS IP Addresses

- For one user uninstalling/reinstalling iTunes resolved the problem

- Try on another computer/network

- Wait if it is an Apple problem