You can delete the core dumps... just stop the vCenter services, delete the files and start the services again.
The following KB explain some situation where the core dumps fill up the /storage/core dump partition on vCSA 5.0: VMware KB: VMware vCenter Server Appliance 5.0 vpxd crashes few seconds after starting
And on KB article you can found the note:
To resolve this issue due to core dumps filling the partition:
- Connect to vCenter Server Appliance console as the root user. The default password is vmware.
- Change directory to /storage/core and run the ls command to check for core files
Note: If there are core dumps, delete these dumps and try to start the service again. The problem should now be solved.