I'm so confused! I bought a new iPhone 5 and it needs iTunes 10.7, but my mac (OS X 10.5.8) won't let me install it!?

I'm so confused. I bought a new iPhone 5, and I want to connect it with my iTunes. But it told me that I needed the updated version (iTunes 10.7) so I went and downloaded that. Now, my Macbook won't let me install the new iTunes because I need an updated version of my OS X 10.5.8 (I bought my Macbook Pro in 2009) !? I'm so confused. Where do I get this new update, and is it going to cost me anything!?