Hi,
for vCenter 4.0 there was a nice excel sheet from VMware to calculate the database size. I guess the numbers are not too far away from 5.1:
www.vmware.com/support/vsphere4/doc/vsp_4x_db_calculator.xls
You can also estimate the size in the vSphere Client (the C# client). Go to Administration -> vCenter Server settings -> statistics. There you can type in your number of hosts and VMs and get an estimated Database size. This is not very accurate, though.
Also if you use the same database for Update Manager, here is an excel sheet to calculate the Update Manager size:
Regards