Q: iPod 5th Gen stuck on boot logo

Force your device to start. To do this, press Sleep/Wake and Home buttons and hold them for at least 10 seconds.

Try to reset your device. This won't delete your data stored on the phone.

• Press and hold the Sleep/Wake button
• Press and hold on the Home button
• Keep holding both buttons until the display turns off and back on with Apple logo on it.

If this does not help, take a look these Apple Support articles:

If your iPhone, iPad, or iPod touch doesn't respond or doesn't turn on - Apple Support

Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support.

As a final step, try the recovery mode. Turn your device off, then plug it to your computer with the home button pressed. You will need to have iTunes installed on this computer. Keep the Home button pressed until you see the iTunes logo on the screen of your iPhone. After that on your computer you should see the iTunes window saying your iPhone needs to be restored to factory settings. Click on the restore button.

More info here: https://support.apple.com/en-us/HT201263