Not all of my music us backing up to itunes?

I've recently brought a new laptop and i'm trying to backup my iphone 5 to the latest version of itunes. A lot of my music hasn't copied. The only music that has been backed up is the songs i've purchased from the itunes store. Is there any way that i could back up all of my music and ready made playlists to my itunes

Try Syncios.

It allows you to transfer stuff from your iPhone to your iTunes library directly.

Also, you can backup your iPhone to pc first then transfer them to iTunes manually.

Personally, I'm using Syncios for months. Really works.
http://www.syncios.com/features.html