iPhone5 - cannot install iTunes 10.7 because I cannot download Snow Leopard 10.6.3

I just got the new iPhone5 for Christmas, but I realized that I need iTunes 10.7 in order to sinc it to my computer. In order to install iTunes 10.7, you need to have Snow Leopard,Mac OS X 10.6.3. However, I have an old MacBook from 2006 (model A1181) that has Mac OS X 10.5.8 and I cannot upgrade to Snow Leopord. Does this mean I will never be able to sync my iPhone5 to my computer? I don't want to have to buy a whole new laptop just so I can access music and manage my phone on my computer, because that would be ridiculous. Where do I go from here?