According tothe info on your Mac, it does indeed support newer versions of OS X. It will support up to OS X 10.8 currently but you must move to 10.6 first.
Going from OS X 10.5.x to OS X 10.6.x is a paid upgrade.
It is no longer officially sold in most stores and if you can't readily find it most customers have been able to get it from Apple by ordering online or via telephone.
For a limited time, it may be available via the Apple Online store in the US:http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard
Alternatively, you can call 1-800-MY-APPLE (1-800-692-7753) and tell them you want the Snow Leopard upgrade which they can send on DVD for around $20 USD shipped.
Once you have the disc, the upgrade process is fairly simple. After the install, keep running System Preferences > Software Update until no more updates are offered and it will also upgrade iTunes to the latest available release.
Once you have 10.6.8 installed, you may be able to upgrade to the latest release of OS X (10.8 Mountain Lion) via the Mac Store. Sadly, you must have 10.6.8 installed first to upgrade further as I previously mentioned.
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Thanks and good luck,