Does Apple still support 10.5.8?
You can see the complete list of Apple security patches at this page: http://support.apple.com/en-us/ht1222

You can see for yourself that the last security patch for OS X 10.5.8 was "Leopard Security Update 2012-003" that was released in May 2012.

There is likely to be a large number of unpatched security holes in Leopard at this point. However it is unlikely that Apple would publish such a list and I'm not aware of anyone else who maintains such a list.

Another issue is that third party software developers may not support Leopard anymore. For example, the current versions of Chrome and Firefox both require a minimum version of 10.6, while the latest version of Safari that runs on Leopard is v5 while the current version is v8. And the last time Safari 5 saw a patch on Leopard was also May 2012 according to the Apple support document above.