Depending on the actual model (there is no G5 Intel) you may be able to upgrade to Snow Leopard. Check the link below for requirements and purchasing info.
If you actually have a G5, Mac OS X 10.5.8 is the maximum it can go, but going past 10.5 won't support the Classic environment that allowed Mac OS 9 applications to run.
If you have a CoreDuo, you are limited to running 10.6.8 with 1 GB of RAM.
If you have a Core2Duo, you may be able to run 10.7.5, or 10.8.4. Neither supports PowerPC Mac OS X applications without special workarounds.