dbelew: you're running an OS X version that is below the minimum version for the current iTunes; current iTunes requires 10.6.8.
You're either going to want to upgrade OS X (assuming your Mac supports 10.6, and 10.6.8 is the most recent in the Snow Leopard series), or do without the iTunes updates.
If your Mac supports Snow Leopard, call Apple directly and order a DVD.
I'm sorry but I find it difficult to understand from this link whether or not my Mac supports Snow Leopard. Would you be able to tell me simply if I tell you which Mac computer I have?
If my Mac does not support Snow Leopard for whatever reason, how will I be able to use it with the newest version of iTunes?
For details of your Mac and its configuration...
> About This Mac > More Info
will provide general details of your current configuration, and will provide very detailed information the further you drill down. (Probably too much information, if you go too far into the tool.)
As an alternative, if you're not familiar with your Mac configuration or with whether it will support this upgrade, consider visiting the local Apple store or call Apple directly, and ask.
Only Apple knows the answer to that second question for certain - whether Apple will add support for this or future versions of iTunes further back than they offer at present - but Apple upgrades software and features somewhat more quickly than other vendors.
The OS X 10.5 series is three versions of the OS behind current, and that's past what Apple usually supports.
The OS X 10.6 release that you're thinking of upgrading to here itself fell off of the general patches and updates availability, and the related software support that was available subsequent to the release of 10.8 release. Apple usually supports the current series and one release back.
And FWIW, the About This Mac displays are considerably improved in 10.7; they'll tell you your specific model when you select More Info...
The other obvious approach here is a new or newer-used Mac.