if you cant do "normal" things with 6GB's, then either there is something seriously wrong with you G5, or your normal stuff is way beyond what most people would consider normal..........
But since you mentioned video editing, yes you are correct that those kind of apps eat ram for lunch.... but they ALSO require very large, fast and clean HDD's, that are NOT the same drives you run your OS & apps from, for storing both their scratch files and the final rendered product.... So if that is what is slowing your machine down, then perhaps you should look into upgrading your HDD's.......
Also, most modern video apps are programmed to use the video card's GPU & vram to do most of the heavy lifting of processing & rendering edited video....so if your video card is older/out of date, that also could be causing some serious slow downs too.........