The DB upgrade probably never happened. You have a cell with the 5.5. bits on it, but the DB upgrade script should not have changed anything given the incompatible error.
Ideally, one would have taken a DB backup after shutting down all the cells and before running the upgrade script. This would be your rollback plan, since you can always create a new CellOS and use responses.properties to align the installed version of vCD code (1.5.x) to your DB (1.5.x schema).
What you should be able to provision a new cell, take the responses.properties from the current cell and install vCD 5.1.3 using the responses file. you're going to do this long enough to upgrade the DB.
># ./vmware-vcloud-director-5.1.3.######.bin -r responses.properties
># /opt/vmware/vcloud-director/bin/upgrade
( or whatever the upgrade script location is)
Once the DB is upgraded to 5.1.3 level, then you run the upgrade from 5.5.x and then start services.