Q: After I've restored my IPhone 5, how do I get my downloaded music back onto my iTunes ?

Is it not on your computer?

Downloading past purchases from the App Store, iBookstore, and ...

You can connect the phone to your computer and sync the tracks from your iTunes library. You can also re-download any purchases from Apple via the iTunes Store and the App Store by going to the "Purchased" tabs and downloaded your stuff.

Perhaps you could try this to resolve your issue: http://support.apple.com/kb/HT4461