I have an iMac G5. The Hardware overview says it is: PowerMac8,2. PowerPC G5. It has 512 MB RAM.
I would like to install a Linnux system on this computer. What system should I use.?
Hello Rebecca - welcome to the Forum.
Have a look at https://www.quora.com/Which-is-the-linux-distribution-best-suitable-for-512-MB-RAM-laptop?share=1 which recommends particularly Lubuntu and Puppy.
Keith
Hi Rebecca - a Google search re: upgrading your model suggests it’s possible to increase RAM to 2.5GB if you have the know-how. See here -
and here -
https://lowendmac.com/2016/getting-the-most-out-of-your-imac-g5
Though lightweight Linux OS’s will run successfully on little RAM, it’s never a bad idea to have more RAM if you can. This will benefit you if you decide in future to go for a more ‘heavyweight’ (ie: more features) distro or if you install additional software to the basic set up. 
If you need help in installing your distro of choice, please post again.
Rich