You should be able to run Snow Leopard on them, but Snow Leopard isn't the latest OS X. Mountain Lion is the current one and will not run on your Mac Pros. I'm pretty certain Lion will work on them, but I'm not sure that would be useful to you.
If your Macs are that old, I would imagine you also have PowerPC software which will not run on Lion or later. PowerPC is the chip that is in the Power Mac G5. In 2006, Apple switched to using Intel chips and has been slowly eliminating PowerPC code from the OS. In the interim, the OS supported what were called Universal applications that would run on either PowerPC or Intel Macs. Snow Leopard was the first big step towards eliminating PowerPC, but it still has an emulator that will let it run the legacy PowerPC-only code.
Given the hardware you have, I would say Snow Leopard would be as far as you want to upgrade until you are ready to invest in new hardware and new software. If you are running Tiger, do you run anything in Classic mode?
Classic refers to the old OS prior to OS X. Those won't work in Snow Leopard.
The Power Mac G5 can only go as far as Leopard (10.5).
If you need to upgrade to Mountain Lion (because you need new hardware), here is a site with compatibility information: http://roaringapps.com/apps:table
You can purchase Snow Leopard on the Apple Store website, but I have no idea where you might get copies of Leopard for the PowerMac G5. You might try calling Apple to see if you can still purchase that. I don't think the installer that cam with the Mac Pro would work on that PowerMac G5.