@Intuition:
I do run Linux on the G5. The situation with Xorg-/drm-/Mesa-bugs got a little better over the last 2 years. My G5 (+ Radeon 9800 Mac Edition) is able to run now X with correct colors and a 2D-accelerated desktop. Firefox works fine too.

However you need a recent toolchain (gcc 7) and software stack for this. No problem on Gentoo which I run, but it is more or less a problem on other distros.

Ubuntu PPC got ditched, 16.04 LTS is the last supported version. Debian PPC ports may be recent enough. There is also openSUSE Tumbleweed for ppc64 (klick). Last time I tried, the iso successfully booted on my G5.