You can run the latest 10.8 Mountain Lion. Usually with any upgrade, acquiring more RAM is desirable.
Note, that you will lose your ability to run PPC applications that you may have currently running in 10.5.
The OS upgrade is not expensive, but if you require other new software as well, there is that additional cost to consider.
Check this webpage for app compatibility with 10.8
http://roaringapps.com/apps:table
More subtly, moving from 10.5 or 10.6 to Mountain Lion moves you into a different marketing model called the App Store (a la iPhone), and second, intends your online experience to be more 'cloud like' with syncing multiple devices, than the traditional Desktop entity you are used to. In this hard to define but subtle change, moving to 10.8 is more than the usual upgrade. It is a conceptual change as well as software.
OS 10.6.8