• Firefox 4 versions and later do not run on a PowerPC Mac.
• Firefox 4 and later require at least OS X 10.5 and an Intel Mac.
• http://www.mozilla.com/firefox/6.0/system-requirements/

For an unofficial Firefox 4 compatible version (TenFourFox) that runs on PowerPC Macs with OS X 10.4.11 or OS X 10.5.8 you can look at:

• http://www.floodgap.com/software/tenfourfox/
• http://www.macupdate.com/app/mac/37761/tenfourfox

Firefox 3.6.x (Mac OS X 10.4 and later) can be found here:

• http://www.mozilla.com/en-US/firefox/all-older.html

I suggest yo change you system requirements: This is what is advertised Operating Systems

   * Mac OS X 10.4 and later

Minimum Hardware

   * Macintosh computer with an Intel x86 or PowerPC G3, G4, or G5 processor
   * 128 MB RAM (Recommended: 256 MB RAM or greater)
   * 200 MB hard drive space

Im running Model Name: Power Mac G5

 Model Identifier:	PowerMac7,2
 Processor Name:	PowerPC 970  (2.2)
 Processor Speed:	2 GHz
 Number Of CPUs:	2
 L2 Cache (per CPU):	512 KB
 Memory:	8 GB
 Bus Speed:	1 GHz
 Boot ROM Version:	5.0.7f0
 Serial Number (system):	CK347009QEB
 Hardware UUID:

SystemVersion 10.5.7 (121) This is way above your so called system requirements This has not solved the problem, but now forces me to use Safari

From which page (link) did you copy those requirements?