Update/fix or recreate old database
Apparently there are updated copies of software called "dBase" but they seem to need special care, and money, to run on a modern OS.  Visual dBase 5.5 itself provides object-oriented and event-driven programming, but I think probably it's mainly based on dealing with one record (row) at a time in the data file (database or "table").  It provides the data storage, and also the program that a user needs to work with the data.

A modern equivalent system might consist of separate programs, a "database server" whose function is only to store data reliably and output it as required, and a "client" or "front end" which presents data in  user-friendly style, typically using the "SQL" language to send and retrieve data on the server (by sets, not individual rows, usually).  Another category of tool, and sometimes an expensive one, is "reporting".

Amongst questions to ask: how many people need to use the data simultaneously?  If it's more than one, then probably a client-and-server solution is best.  If one, you might be able to do the whole thing in Microsoft Excel.

Your employer may be able to buy a database application which serves the needs of your industry, and save the effort of re-learning the one that you've got or writing your own - your time presumably costs money as well.  But it won't be cheap.  A buy-in will probably be based on one of the industry-standard database servers that are known here, and you can probably convert your data into forms that the system will accept.  And the tool may provide definable fields for data that only your employer has thought of storing.

So, you could start by identifying any suitable database products for your industry, find out what database server they may use, and whether the server comes as a cheap or free download for tryout use - and then first of all, get that server, and try to import an initial copy of your data, your way, into the server.  That should move you towards converting the data for use in the new database product, or else writing your own program again, if you think you can do it.  If this exercise doesn't work, then, look at a different software and server package - or look at hiring a database consultant to help you.

But if you urgently need to replace the existing system, then using an updated version of dBase may be easier, after all.  It won't be an identical system to what you've got, but I suspect it doesn't represent twenty years of progress...  so maybe it won't be so different after all.