It's been so long since I've touched Netware 5.0, but here are your two strategies but I can't verify either one or how to specifically carry them out. Need someone who worked with Netware 5 more than I to give better advice.
1. USB connection to a memory stick or an external USB drive attached to the server. I don't have much hope for this one, since USB drive support was pretty scarce in the Netware 5 days.
2. Get a bootable Linux CD that can access Netware Traditional (not NSS I'm assuming) volumes. Then you could attach an external drive to the server before booting and copy data to the external drive.
3. Get a new network card, install the drivers and see if you can get REAL networking going. That's your best approach and more within the limits of Netware instead of going "outside" the actual operating system.
If the problem is not the network card/driver, maybe it's your switch that's connected to the server. Try a different switch or connect a client directly via a cross-over cable to the server.