My computer won't download iTunes?

I just got an iPhone 5 yesterday and I'm trying to put music on it. When I plug it in to my computer a pop up comes up and says "Can't be used because it requires iTunes version 10.7 or later. When I go to download the new version of iTunes, (I have a mac) a pop up comes up and says "This software requires Mac OS X version 10.6.8 or later." So can I like never get music on my phone from my computer?

Unfortunately, the solution to this problem requires $19.99.go to the link below and you'll have to upgrade and buy the OS X to the latest version.

https://itunes.apple.com/...ls=1&mt=12

P.S. Sorry, but this is just what i think. I do not own any macs!