If you're having problems rebooting an iPod Touch 5th generation, then try pressing the power button and home button at the same time.
When the 'power off' slider option appears, ignore it and continue to hold the two buttons. Unfortunately, you may have to do this several times, as there can be issues with this method of rebooting.
- Go to Settings > General > Reset and tap "Reset All Settings"
- Your preferences and settings will all be reset, but you won't lose music, contacts, calendar etc.
Another option is to restore from back-up or restore to factory settings.
Hopefully by now your iPod Touch will be working again, but if there is still a problem it might be time to make an appointment at the Genius Bar of an Apple Store.
Good luck!
