How can I copy my music from iPod Nano (model A1446) to iPhone 5s?
I've had a similar problem. The only solution I found was an application called TouchCopy12. It allows you to transfer songs off of an iDevice directly to iTunes. I'm pretty sure you are able to transfer playlists as well. You get (I think) 82 transfers before you have to register. The link to the program, as well as information about it, will be located down below. I hope this helps and good luck!

http://www.wideanglesoftware.com/touchcopy/purchase.php

and

http://www.wideanglesoftware.com/touchcopy/features/index.php