I dont think the 1999 macs had Firewire, could be wrong though.
I take it the iMac is running OS X?
If so:
Your best bet would be to link the two machines with an ethernet cable.
You may need a crossover cable, if you've only got one machine, I wouldn't expect you to have one, so its best to go out and buy one. Although, as previously stated, a standard ethernet cable (CAT5) may work.
You'll need to give the macs IP addresses.
Start with 192.168.1.1 for the G5 and 192.168.1.2 for the iMac. The subnet mask should be 255.255.255.0 and the gateway/router should be 192.168.1.1
Apply the settings, and then on the iMac, go into system prefs > sharing and enable personal file sharing.
Go over to the G5 and click on your desktop, cold command and press K.
Type in the connect box "afp://192.168.1.2" without the quotes, and hit enter.
The rest should be self explanatory 🙂