If you search on the internet there are devices that converts serial to ethernet.
This is one, the Compoint - LAN adaptor
But not sure if this works right out of the box, or if there needs to be a special driver for it. Most likely you will need a dedicated driver I think.
This is the product link:
http://www.ak-nord.de/en/produkte/compoint.htmYou might also maybe find this page interesting.
http://www.cs.rose-hulman.edu/~gunnbr/enetAmiga.htmlIts quite old, not updated since '95, but still useful.
Its describes a few sidecar otions about how to get ethernet on the A500.
good luck