Likely 10.5 would slow it down, yet is the latest OS you can run, 10.4 might be a better choice.
So we know more about it...
At the Apple Icon at top left>About this Mac, report the version of OSX from that window, then click on More Info, then click on Hardware> and report this upto but not including the Serial#...
Model Name: eMac
Model Identifier: PowerMac6,4
Processor Name: PowerPC G4 (1.2)
Processor Speed: 1.42 GHz
Number Of CPUs: 1
L2 Cache (per CPU): 512 KB
Memory: 2 GB
Bus Speed: 167 MHz
Boot ROM Version: 4.9.2f1
To use Mac OS X 10.4 Tiger, your Macintosh needs:
* A PowerPC G3, G4, or G5 processor
* Built-in FireWire
* At least 256 MB of RAM (I recommend 1GB minimum)
* DVD drive (DVD-ROM), Combo (CD-RW/DVD-ROM) or SuperDrive (DVD-R) for installation
* At least 3 GB of free disk space; 4 GB if you install the XCode 2 Developer Tools (I recommend 20GB minimum)
See Tom's, (Texas Mac Man), great info on where/how to find/get Tiger...
Or Ali Brown's great info on where/how to find/get Tiger...
* Mac computer with an Intel, PowerPC G5, or PowerPC G4 (867MHz or faster) processor
minimum system requirements
* 512MB of memory (I say 1.5GB for PPC at least, 2-3GB minimum for IntelMacs)
* DVD drive for installation
* 9GB of available disk space (I say 30GB at least)
Classic/OS9 Apps no longer supported.
Trouble is Apple no longer sells it, check eBay & such for the Retail version, not the Gray Discs...
There are workarounds if the 867MHz CPU is the only hangup...
List of Applications Not Compatible with Leopard...