Firefox 4 says it's not compatible with my Mac OS 10.5

First Firefox 4 is old now and two you have a PPC Mac. As of Firefox 4.0 and newer a Intel Mac and OSX 10.5+ is required.

The last version from Mozilla to work on PPC Mac is the Firefox 3.6.* where the current 3.6.22 can be found at http://www.mozilla.org/en-US/firefox/all-older.html

If you want to use say Firefox 6 then either you can build it yourself or use a third-party build from http://tenfourfox.blogspot.com/2011/08/601-now-available.html

I have 10.5 just installed.

You may have OSX 10.5.8 however your useragent in More system details... on right of your post shows you have a Power Mac, not Intel.

So basically you can either use Firefox 3.6.22 or the third-party build mentioned.

http://www.mozilla.org/en-US/firefox/3.6/system-requirements/

http://www.mozilla.org/en-US/firefox/4.0/system-requirements/
http://www.mozilla.org/en-US/firefox/5.o/system-requirements/
http://www.mozilla.org/en-US/firefox/6.0/system-requirements/

Mac Recommended Hardware

   Macintosh computer with an Intel x86 processor