To upgrade Zonemaster-Backend from versions 4.0.x to versions 5.0.x you have to upgrade the database:

MySQL (or MariaDB)

Run /usr/local/bin/patch_db_mysql_for_backend_DB_version_lower_than_5.0.0.pl

PostgreSQL

Run /usr/local/bin/patch_db_postgresq_for_backend_DB_version_lower_than_5.0.0.pl