its my experience... dealing with having 10.5 myself that i had to update OSX using downloads from here to get beyond a certain level i believe i am at the end of the 10.5 update extent...
but after that.. i needed programs that were "older" in nature to work on the OS...
i found a site that collects "Old Apps" for bot PC & MAC.. and they actually have slightly older versions of browsers that work and will update to a point and will still work....
the site ... http://www.oldapps.com/
i recommend Firefox myself as it is what i use... and it works really well... but you will need to make sure you also do any and all updates you can find here at the "App Store" for instance Quicktime up to 7.7 and then you also need to make sure you update flash player (on your own) to make sure it works properly... even tho you will get notices from some websites saying that "you need to update your browser"... which you dont... and kinda cant to a point... (trust me i know on this one...lol)...
the site for the flashplayers is .... http://www.adobe.com/shockwave/download/alternates/
dont try to use the most recent version it wont work on 10.5
and after you are all done with that... it should work a little more smoothly and better...
LASTLY... you should try at some point to find a copy of a 10.6 install disc and "upgrade" like i plan to soon....
I HOPE this helped in some way.... leave me some feedback