Hi Laurel, My Name is XXXXX XXXXX I look forward to assisting you today with your question.
Good News ! Your Mac can handle the latest Mac OS X 10.8 Mountain Lion
To install Mac OS X 10.8 Mountain Lion, you need to have the Mac OS X 10.6 Snow Leopard installed on your Mac. So first, buy the Mac OS X 10.6 Snow Leopard Retail Discs
and upgrade your Mac to 10.6 Snow Leopard from 10.5.8 Leopard. Upgrading is easy, just put the discs to your Mac and follow the onscreen instructions to upgrade.
You can't download 10.6 from Internet, so you need to buy 10.6 Snow Leopard as discs to upgrade.
You can buy the Mac OS X 10.6 Snow Leopard Retail
discs from eBay.com, Amazon.com etc or from Apple. See here : http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard
After installing Snow Leopard, do all Software Updates from Apple > Software Updates
and then you can buy 10.8 Mountain Lion from Snow Leopard's AppStore application as digital download. (There is a AppStore application where you can buy applications directly from your Mac itself as digital download)
You can directly install 10.8 from 10.6.8 without going through 10.7
If you have any questions or would like any additional information, please don't hesitate to ask.