As far as I understand it, dbmopen in perl4 used whatever DBM package you had installed. In perl5, you can explicitly state which DBM package you wish to use, using the tie function. So you should still be able to use the DBM files that you created by using perl4. Do you know which DBM package you used?

Take a look at AnyDBM_File, which provides a "framework for multiple DBMs" (and also has a nice list of the pros and cons of various DBM packages--DB_File is generally the most highly recommended); and tie, the mechanism by which DBM files are used in perl5.