Ah yes, no updates are available for 10.5.8, & 10.5.8 won't handle all the new stuff for iPhone 5s.
You need a Paid Upgrade if your Mac can handle it, though it's cheap... $20.
Snow Leopard/10.6.x Requirements...
* Mac computer with an Intel processor
* 1GB of memory (I say 4GB at least, more if you can afford it)
* 5GB of available disk space (I say 30GB at least)
* DVD drive for installation
* Some features require a compatible Internet service provider; fees may apply.
* Some features require Apple’s MobileMe service; fees and terms apply.
Which apps work with Mac OS X 10.6?...
It's been pulled from the online store & Apple Stores, so you have to call Apple to buy it, last I heard.
Buy Snow Leopard > http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard
Call Apple Sales...in the US: 1-800-MY-APPLE. Or Support... 1-800-275-2273