Unfortunately, no.
Older Macs, like your G5, were based on the IBM PowerPC processor which uses a completely different architecture than the x86-based Intel processors.
Several years ago, Apple faced a serious dilemma... the IBM PowerPC chip was becoming obsolete. IBM was falling behind in the design of the chips, especially in the low-power portable CPUs needed for laptops. Apple had a choice: remain loyal to the IBM CPUs that they had built their systems on for years and fall way behind Windows-based PCs that were using x86-based Intel chips that were starting to pull way ahead in clock speeds OR change the entire architecture of the Mac computer to use Intel chips and "keep up with the Joneses."
Apple chose to abandon the PowerPC CPU and convert their entire architecture to utilize Intel chips. In order to support the new hardware, OS X was developed with core support for Intel-based processors. With OS X, the PowerPC CPU was a thing of the past.
Since Snow Leopard is just a revision of OS X, it requires the newer Intel-based Macs in order to run. OS X will not support the older PowerPC-based Macs.
And since all the hardware inside Macs was changed in the move from PowerPC to Intel, there's no way to upgrade the hardware in your G5. The motherboard and system hardware don't have the right sockets and chipsets to run an x86-based Intel processor.
Unfortunately, if you want to use Snow Leopard, you're going to HAVE to buy an Intel-based Mac computer.
***ADDITIONAL INFO***
The poster below is both right and wrong.
I had forgotten that earlier versions of OS X did have support for both "flavors" of Macs, both PowerPC and Intel x86. It wasn't until Snow Leopard, specifically, that support for the PowerPC processor was finally dropped all together:
http://arstechnica.com/apple/news/2008/06/snow-leopard-to-be-intel-only-but-not-64-bit-only.ars
However, the good news with that is that you can install any flavor of OS X up to Snow Leopard on your older G5.
Where I disagree is with the statement that the new Macs (and the processors) are not x86 architecture. While the way a Mac UTILIZES processors is different that the way a PC utilizes a processor, the processors themselves are standard, off-the-shelf x86 processors... the same x86 processors you'd find in any PC. It's not the COMPUTER's architecture that is x86, it is the processor's architecture that is x86... and that standard is across the board, even including AMD's Athlon designs which are also based on the x86 architecture. Intel is NOT making special processors for Apple... they are simply sending Apple shipments of the exact same processors any vendor OR hobbiest PC builder could buy:
http://www.9to5mac.com/intel-apple-534093460