It is almost impossible to find USB adapters (capable of handling the latest security standards) for Mac OS X 10.3 and earlier. Regarding USB Wi-Fi adapters: It is absolutely necessary to have drivers compatible with the Mac operating system. Instead of 'normal' file sharing, it is possible to set up a G5 as an FTP or web server, allowing access to files on a more modern computer using an FTP client or a web browser. Set up file sharing on Mac - Apple Support See also the following article if the MacBook Pro shall be shared: MacBook Pro (Retina, 13-inch, Early 2015) - Technical Specifications
Mac Help could be useful when connecting a 10.14 MacBook Pro to a shared volume on another computer. BTW, which exact G5 model and operating system version are you using?
Details about the TCP/IP configuration and file sharing setup should be available via the Mac OS X help. If the G5 is close to the router, you could just connect a plain Ethernet cable to a free LAN port.
