You can try using tenfourfox, which is not an official mozilla product but is maintained by the community, http://www.floodgap.com/software/tenfourfox/

Mozilla no longer supports the PowerPC, the last version of Firefox that runs on PowerPc is Firefox 3.6.28, but that has been discontinued. For details on that see Firefox no longer works with Mac OS X 10.4 or PowerPC processors

As for other options, they appear to be very limited, this link may help - http://macpowerpc.com/2012/11/27/browsers-updated-on-powerpc/

These browsers are made by individuals or small groups working together rather than browser vendors. They are based on opensource browsers, for example the first 2 in the list are based on Firefox. They may have reduced functionality, for example TenFourFox does not let you run plugins such as Flash.

I read in a thread elsewhere that due to the inherent security risks of running Safari unsupported, it would be better to run a beefed up browser like Mozilla Firefox - I'm using Aurora and so far so good on a G5 running os x 10.5.8 but I also read that TenFourFox was good too so your preference. Good luck! Aurora download:

http://xxxxxxxx.xxxx.xxx/Mozilla-Firefox-Aurora/3000-2356_4-75446901.html

[edited by moderator - please only post links to the official Mozilla server]