Basically, a lot of people build themselves a Hackintosh then Dremel and duct tape it into a G5 case.
It's do-able but then you've got to deal with all the Hackintosh issues such as:
1- Tricking Apple software into thinking that your generic parts are a Mac computer of some sort. Easy right now, but Apple doesn't approve and may take stronger steps to discourage this.
2- Choosing parts that can not only mimic a Mac system but actually fit in the case, not sound like a jet on takeoff, not overheat or otherwise go "Boom!" and of course cost less than that nice, new Mini at the Apple store.
3- Using the system in any sort of professional capacity such as developing iPhone apps. This can cause legal problems later on even if you somehow manage to get away with it right now.
4- Selling the system to anyone other than a Hackintosher can present a pile of problems. Unless of course you sell it as a Linux or Windows PC in which case you just get the "normal" problems.
Unfortunately, the G5 has suffered the same fate as most older Apple products, (or for that matter any other older computer of ANY brand) a near total collapse of value. That stunningly stylish, solidly built wonderful case is of greater value than the system itself.
My advice is to sell it on eBay for what you can get and buy a new Mac. Even the lowly Mini is a better bet.
2nd choice would be a 1st or 2nd gen Mac Pro. But these are still commanding quite a bit more than your G5 might get.
Unless you're a good hobbyist and tinkerer it's just not worth chopping it up. If you were, you probably would have already done so.
Save up and get a new one and avoid a bunch of expense, bother and minor lacerations.
Have Fun,
Keri
PS. Another reason not to Hack it yourself: Any Hackintosher that might be interested in buying your G5 is going to want to do it themselves. Also, you'd probably never sell it for more than the parts cost plus what you could have gotten for it untouched.