How do I sync unpurchased songs to iphone

I just got a new iphone for Xmas, the 5c and I dont know how to sync songs I didn't purchase. I can download the others just fine using the phone but in order to get the others, I have to hook the phone up to my mac laptop.

My mac laptop version is 10.5.8 so I can't download the most recent itunes. And updating or getting a new mac is totally not an option right now. Im pretty sure thats a big issue.

How do I sync my unpurchased songs??? Im so distressed...😢