Here's your dilemna:
OS 10. 5 was the FINAL "Universal Binary" build of OS X that Mac ever made - meaning it ran on PowerPC and Intel Macs. Because of that, software (including Flash Player) for OS 10.5 was of a different framework to be compatible with either processor architecture.
THAT's the most recent build of Flash Player that will run on 10.5.8. Unfortunately, most Flash content today requires 11.2 or higher, and it simply isn't available for your OS. This is the computing world's way of telling you that OS 10.5 is becoming obsolete, if it isn't already. That's the bad news.
The good news is: While your OS may be obsolete, your Mac certainly isn't. You can upgrade to OS 10.6.8 (and unfortunately, due to the age of your Mac, that's as far as you can go - OS 10.7 or 10.8 require a 2010 or newer Mac to install) for just $20: http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard OS 10.6.8 WILL run the latest Flash Player and will allow you to access web content for a few years to come. That's a lot cheaper than going out and getting a new Mac.