Hello and Welcome to the Support Community
Mac OS X 10.5.8 is an update to Mac OS X 10.5. Treat this like a service pack like SP3 for Windows.
You can't apply a service pack to Windows, without Windows being installed.
You may Have Mac OS X 10.4 installed currently. In order for you to run 10.5.8 you need to install Mac OS x 10.5.
This can't be downloaded for free, you have to by it on DVD and install it.
It's called Mac OS X 10.5 leopard.
You can buy it from venders like Amazon or eBay. It's not cheap to buy