If you are trying to restore your iPod 5 and getting a message that states, “iPod busy, can’t restore” then you will want to go through a few steps to make sure you can get past that message. The first thing to do is make sure your iPod 5 is fully charged. If it is charged, or after you have charged it, then make sure all the apps that might be running in the background are shut down. To do this, double click on the Home button. That will allow you to swipe your screen left or right to view the apps that need to be closed. Swipe each app upwards in order to close it.

When all apps have been closed, you can restart your iPod 5 by holding down the Hold and Home button at the same time. After the screen flashes and goes black, wait for about 60 seconds and then hold the Hold button down until you see the Apple logo. Before attempting to restore iPod 5 from this point, make sure you have backed up all data to iTunes or iCloud and that you are running the latest iTunes version.

Source Apple Support