Your next step will be to upgrade to Snow Leopard (10.6). Check the Apple link below for requirements and purchasing info.
You have to understand the difference between an Update and an Upgrade.
An Update is a free change to add to the base code or as a bug fix within an existing Operating System. Such as the .8 added to 10.5.
An Upgrade is a complete new Operating System that must be purchased. Such as 10.5 Leopard to 10.6 Snow Leopard.
10.5 Leopard was written for Power PC Macs with code added to force it to run on Intel processors.
10.6 Snow Leopard has completely rewritten code and only runs on Intel Macs.
10.7 Lion used some 32 bit which allows it to run on Late 2006 through Early 2008 MacBooks and a lot of 64 bit code.
10.8 Mountain Lion is pure 64 bit, which excludes more systems than Lion did. It can only run on the Late 2008 through Mid 2010 MacBooks. It's not something you can add memory to, for example, as it involves the base architecture.
To see which model you have go to the Apple in the upper left corner and select About This Mac, then click on More Info. When System Profiler comes up check the Model Identifier