Preferably, you want the Mac using the system to do the install. However, with Mac OS X (unlike Mac OS 9), the system is complete. I wanted to try Leopard on my old PowerBook G4 (not officially supported so cannot install directly). I used my PowerMac G5, with the PowerBook in Target Disk Mode, to run the installation, and it worked. And Leopard is Universal, so the other Mac can even be an Intel Mac (as long as it can run Leopard). I had a small external FireWire drive that I used as a maintenance startup disk, and it could boot my PowerPC Mac and Intel Mac. I would have advised doing it the reverse way (with other Mac in Target Disk Mode), except you already told me the iMac G5 was not seeing anything connected to the FireWire port.
You didn't tell me what your other Mac is, so it may not work at all, if it's too new to boot the Leopard install disc from its optical drive.
Here's another idea that might work (although I've never tried it this way). In Leopard, you can add a partition to an existing drive with data, without erasing the data. Use Disk Utility to add a small partition to the iMac G5's internal drive. 10GB should be enough. Then, use Disk Utility to Restore the Leopard installation disc's disk image to that small partition. When that's complete, eject the disk image and set System Preferences Startup Disk pane to start up from the small partition (which is now a duplicate of the installation disc). If you can get the iMac to start up from that partition, run the installation targeting the other (primary) partition that currently has Tiger.
NOTE: You should not do this if the iMac's current internal drive volume has low free space remaining (50GB or more should be good to add a 10GB partition). Adding a partition involves moving existing data on the drive, to clear out a contiguous area on the drive media (at the "end" of the drive) that is at least (in this case) 10GB. The more free space you have, the better, for this operation. If you don't have a recent backup of the iMac's internal drive, you should do one before adding a partition. You should already have a backup, since you are trying to do a major system upgrade, which is also somewhat risky.