If you are running 10.3.x the last free update available for it was made on February 2008:
10.4 and 10.5 can be installed on most iMac G5s, provided you are prepared as these tips suggest: https://discussions.apple.com/docs/DOC-2541 - for 10.4
https://discussions.apple.com/docs/DOC-2275 - for 10.5
Note if you update past 10.4.11 (10.4.0 through 10.4.10 are older) the partition that is updated will not be able to use Classic.
Note, you will not be able to update your machine past 10.5.8.