The only reliable way to work with and possibly export old .fp5 databases and save them as .csv files would be to use the very software they were created in - FileMaker Pro. Seems the support for older FileMaker format is pretty limited, so this may not only be your best, but also possibly the only way to convert FP5 to CSV.
Convert FileMaker Pro database file to Comma Separated Value.
We found 2 software records in the database related to .fp5 to .csv file format conversion.
Microsoft Windows software - convert fp5 to csv on Windows
A program used to create and manage information databases
Convert from fp5 file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned fp5 to csv. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Apple macOS / Mac OS X software - convert fp5 to csv on OS X
A database management program for Mac