The internet on PowerPC processors is a very wierd experience. Apps like tenfourfox that focus on optimizing the web for the older CPU's do a good job but i've found they use a lot of resources and make the machine unusable when they are running (keep in mind that is is the performance on my iBook, on a different machine it may be much more different) .So i made a little experiment, will an older version of TenFourFox work better than a newer one. Conclusion of that experiment is an obvious: duh. It runs waay better than the newer one and it even supports QuickTimeEnabler which allows us to watch youtube videos at 480p with no issues.
When it comes to the internet itself, i found that it is best to use mobile versions of websites (if you have them) eg. Facebook and Twitter. Websites like 4chan and Reddit that dont use as much resources should run fine in desktop mode. YouTube without quicktimeenabler is out of the question but it may be work on a G5. Overall the browsing experience on a PowerPC machine is good but slow.
Your browser options are:
Firefox
TenFourFox ( If youre running the older version its both supported and pretty fast!)
Opera (Slow and unusable)
Safari (Fast but extreeeemly unsupported)