Iphone 5 says it won't sync because my mac requires itunes version 10.7?

And then when I try to download the itunes, it says my mac needs 10.6.8. How do I fix this?

All answers are greatly appreaciated, thank you.

You don't say which Mac OS version you currently have. However, most likely you have 10.5.8, which is Leopard. You need to buy and install at least Snow Leopard, which is 10.6. (You will be able to update to 10.6.8 once you've installed Snow Leopard itself). You can find it on Amazon.com and eBay, but not through Apple any more.