I seem to recall the 5200 had an optional expansion card for Ethernet, otherwise you are stuck with using a dial-up Modem for network connections.
If you have only a modem, and another computer with a modem, you can do a file transfer directly over a modem-to-modem connection if the two computers are running ZTerm or MacKermit, you just hook the modems up to each other, have one "dial" the other and the other will answer.
If you have Ethernet and a LAN, then you can use Personal Web Sharing (HTTP) and download the file like you would from a web site, where the 5200 is the web server. An other method is File-Transfer-Protocol, remember Fetch? You can set up an FTP server using NCSA Telnet or BetterTelnet.
Might be hard to figure out how to use those for a newbie, but they were pretty common tools in the university environment about 25 years ago.
I had one of those external SCSI SyQuest EZ135MB drives that I used with the 5200 and a later model G3 which also had SCSI, you might be able to find a used Iomega SCSI Zip 100MB drive and another newer computer with a FW/USB Zip drive interface as an alternative to moving the files from the 5200 to another computer.
The SCSI version should be compatible with PC/Mac. If your PC does not have SCSI, you might have to get a USB version for it, then the drives should be compatible with both.
They have a 250MB cartridge also.