It's not a complex process at all.
First, to be absolutely safe, back up important documents and images to Cds or DVDs. This is extra insurance.
Then, make a clone of your current Mac to the external drive. You can of course just save all your files and folders (including images) to the external drive, but a clone is much more effective, as you will see in a moment. A clone is an exact copy of your old computer.
To make the clone, download SuperDuper, a free app and follow the apps instructions - its really very easy.
Once the clone is made, do not yet erase everything from your G5.
When you get your new Mac, set it up close to the old one. Turn on the new Mac and run through all the se-tup procedures. At one point, it will ask you if you want to transfer files and settings from another Mac. Select yes, and follow the instructions.
(The instructions will tell you to connect the 2 Macs with a Firewire cable, then to restart the older Mac while holding down the 'T' key. This turns the older Mac into an external hard drive. You then select the User Accounts you want to copy to the new Mac, and away you go. I do this several times a week for clients, works beautifully.)
The result is that when you finish setting up the new Mac everything will be as it was, right down to your desktop picture, web bookmarks, applications, files and folders.
Then erase your the stuff on your old Mac (if you are concerned about security, check out the options in Disk Utility, which can really clean it).
Then all you have to do is enjoy your new Mac. Tough life.
P.S. The reason for making the clone of your original drive is to ensure the option of migrating from that drive should something happen to your G5 drive. Also, as a by the way, the application that does the transfer is called Migration Assistant and it is in the Utilities folder of your Applications folder, and can be used at any time to transfer accounts between Macs.