The new vSphere Web Client in vSphere 5.1 supports both vCenter Server 5.0 and 5.1, but before you can connect to a 5.0 system, you will need to manually register the vCenter Server with the vSphere Web Client Admin Tool. In the previous release, you could register a vCenter Server using the Admin Tool which was available by connecting to the localhost web application as outlined here or by performing the same operation via the command-line using /usr/lib/vmware-vsphere-client/scripts/admin-cmd.sh on the VCSA.
It looks like with the latest release, the admin script no longer function ("Cannot connect to vSphere Web Client administration tool.") and since the VCSA does not contain a full blown desktop with a browser like it's ugly Windows cousin ... you will not be able to register any of your existing vCenter Server 5.0 systems. Luckily, you do not need a browser running on the VCSA to perform the registration, you can use the browser on your desktop by simply using SSH port forwarding.
In the example below, I am connecting to my VCSA 5.1 from my iMac via terminal. You will need a system that can reach your VCSA that has a web browser which will be used to access the Admin Tool.
Step 1 - SSH to your VCSA using the following command, be sure to replace "172.30.0.194" with the IP Address or hostname of your VCSA
ssh email@example.com -L 9443:127.0.0.1:9443 -N
If the port forward was established correctly, the prompt will just sit there as denoted by the screenshot below.
Note: If you wish for the prompt to return, you can specify the -f flag after "ssh" but this ensures you remember you have a port forwarded.
Step 2 - Open a web browser on your local desktop and connect to the following address:
This should launch the vSphere Web Client Admin Tool and allow you to register your vCenter Server 5.0 hosts.
Even though I was able to get this to work, I personally would still prefer to be able to perform this operation via the command-line. I am still hoping that I might have missed something, but I have been told this might be expected