Mac osx update what's going wrong?

I just got a iphone 5, i plugged it into my itunes and it said i need to update my itunes. I updated it but it won't install because it says that i need to update my mac software.right now i have 10.5.8 when i check for software update the new mac osx isn't there and i have tried downloading it from the apple website but it says it require 10.6 i dsont know wats going wrong as this has never hapenened i just want my phone to work please help!

You need to buy a copy of the Snow Leopard (10.6) installation disc. You can still find copies at Amazon and eBay.

The requirements for iPhone 5 clearly state:

Syncing with iTunes on a Mac or PC requires:
Mac: OS X v10.6.8 or later
PC: Windows 7; Windows Vista; or Windows XP Home or Professional with Service Pack 3 or later
iTunes 10.7 or later

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