Can't update iTunes with my operating system...

I just upgraded my phone to the 5s and came home to sync it with iTunes and was told to update iTunes to 11.1. Well, my operating system won't allow me to update to 11.1, so I don't know how I'm supposed to sync my phone. Am I just out of luck???

My computer is running OS X 10.5.8 right now, if that helps. I purchased my computer in January 2008, so it's an older model. Any help that you can provide will be greatly appreciated.

Thanks!

Anna