I'm surprised that you're not noticing lag times running 10.5.8 on an older computer, and finding websites not crashing. I had an iMac that I had upgraded to 10.5.8, and I finally moved on because even with FIOS things were slow.
That being said, I'd do nothing -- just keep all the software versions that you're using now and treat your laptop like a static system. If it ain't broke, don't fix it. Don't try to upgrade anything that still works well. All "unsupported" means is that Apple and Firefox will not be putting out any more patches to the OS and that browser. They won't be testing new products to ensure that they will continue to work with your computer.
Are you playing with fire? Eh, possibly but not too much. There's only been one real crisis with Java in the last year that actually was a problem. The solution for the most part is to disable Java. See the following article about some of the issues.
http://www.macworld.com/article/1168358/java_security_threats_what_you_need_to_know.html
Does this mean that you couldn't ever have a problem with the older software? Of course not. But the risk is low, the number of people targeting old Mac OS versions is small, and many of the kinds of viral attacks that make PCs go wonky don't work against a Mac. Turn on the maximum firewall protections that you've currently got.
If it were me and I decided it wasnt' time for me to upgrade my computer right now, I'd be okay working on the closed system. Just make sure you keep backups of key files, and keep some older versions around (as you never know when the virus hit your computer and may have to go back in time to get the "clean" version of a file). That's smart in any case, because it's far more likely that something else will die before you get hit by an irrecoverable virus.
And for the most part on macs, you just need to save the files, not an entire clone of your OS. If you have to restore, you want clean copies of all the OS and programs anyway, so you just need to save the unique docs and items you have.