Mac Software update for iTunes?

My macs version is 10.5.8.
When i connected my new iPhone 5 to iTunes, I was unable to sync with iTunes because it said my software was not up to date. However, I have nothing under the software update window. How do I update so that I can sync with the iPhone 5?

Added (1). I have Itunes 10.6.1(7)

Go To Update Website Of Mac Or Itunes It Will Help You Or You Can Teke Help Of Google!