Is there any way to transfer music from the old iTunes to iPhone 5S?

I am still using my old macbook, version 10.6.?? (forgotten), I don't intend to upgrade the OS X, since everything is working fine. So the iTunes in it is also the older version, since my software doesn't support the new version of iTunes. And thus, I can't get my music into the iPhone 5S that I've just bought. Any kind souls that can help me with this?