Q: how can i download my apple music songs on my iPod nano 5th gen?

You can't.  iPod Nano's do not support Apple Music's DRM protocol (No internet access)

You can’t.

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You don't own the music that's downloaded for offline listening (but which allows you to listen to the music without wifi access), and copying it to other devices would lead to copies being made of that, and so on, which would be "stealing" since you don't own the music in the first place, you're "renting" it from Apple as long as you pay the $9.99 monthly fee.