Why won't my iPhone 5 sync my music?

I got an iPhone 5 in December and I have not been able to sync my music onto it from my computer. First of all, I have all my music on iTunes on a PC, even though I own a Mac. I have since gotten some music on iTunes on my Mac but every time I plug my iPhone into my Mac, iTunes says it is unable to sync because I need to get the newer version. So when I go to download the newer version, it works, but then when I go to install the new version of iTunes, it says it can't be installed because the "software requires Mac OS X version 10.6.8 or later" which I have no idea how to do. I don't know if it means my Mac is too old, which it shouldn't be, because I bought it less than two years ago. Can someone help me out? All I want to do is sync my music onto my iPhone! But it seems like I have to go through a bunch of steps before that can happen.

It sounds like your mac software is out of date.software updates frequently so here's a link for how to check if your computer needs to be updated. If and when it does, update it then you should be able to download itunes.

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