You're problem is you purchased a PowePC Mac computer. Apple left the PowerPC processor and architecture behind in 2006 when they switched to Intel cpu's and associated architecture. For awhile, there was software being coded for both systesm, but as the Mac PowerPC has faded into history, and Intel Mac's came into their own, many developers have simply dropped all software support for PowerPC systems.
You will need to use archival sites to find older releases of software compatible with PowerPC.
for some you will find material
e.g. adobe reader - http://www.adobe.com/support/downloads/detail.jsp?ftpID=4977
firefox - http://www.oldapps.com/mac/firefox.php
But you will have to search for such versions, and for some software, you simply will not find anything available for PowerPC.
P.S. you also cannot update your OS X as 10.5 was the last release for PowerPC. OS X support for PowerPC machines officially ended with the release of OS X 10.6 (Snow Leopard) in 2009. The emulation layer, Rosetta, was then finally dropped with OS X 10.7 (Lion), and Apple ended parts service and support for PowerPC machines in 2013.
