Unable to carry out Software Update on OS X 10.5.8 I have tried to carry out a Software Update on a Mac running OS X 10.5.8.

My first problem is that I am unable to find the Mac App Store on this computer (whether by using the search function or looking in the Applications folder.) 

Even when I go to the Apple website and attempt to get redirected from there to the Mac App Store to find the Software Update, nothing happens.

Furthermore, the computer does not detect any Software Updates when clicking on the top-left Apple menu and selecting Software Update.
Mac App Store requires OS X version 10.6.8 or higher to install. You can try updating via USB (paid upgrade) if you have an Intel x86 based processor.