VMware vCenter Server Appliance 5.5.0a released
I have John to thank, from his heads-up comment. Here's the 2 VMware links you're looking for:
vCenter Server Appliance 5.5.0a | 31 OCT 2013 | Build 1398493
Appliance Version 5.5.0.5100 Build 1312297 is what was current, right up until Nov 01 2013's release of 1398493. I don't really want to download and re-install the appliance though, I prefer to use the "Check Updates" button over on the VMware vCenter Server Appliance Web UI:
https://vcenter:5480/#update.Status (where your hostname replaces my vcenter name)
You may want to grab a snapshot of your VCSA (VMware vCenter Server Appliance) before you begin, in case you have an issue that requires roll-back.
Next, just click the "Check Updates" button, with the entire update procedure taking about 15-20 minutes for my lab, with 4GB allocated of RAM in the VM, thin-provisioned on a SATA3 SSD.

Oct 31 2013 Original Article:
Documenting an issue that has now been resolved.
Unfortunately, when I click the button, after about 45 seconds, I get this error:
Failed to check for updates(Error downloading manifest. Please contact your vendor. Couldn't resolve host 'vapp-updates.vmware.com' URL: https://vapp-updates.vmware.com/vai-catalog/valm/vmw/8e70f769-fd50-4a7a-bee2-2c0d945e23b0/5.5.0.5100.latest/manifest/manifest-latest.xml) on Saturday, November 2, 2013 11:56:39 PM GMT-04:00
Perhaps in a few more days, VMware will fix this, with an adjustment to manifest file or something along those lines. Meanwhile, anybody have any ideas, as far as a way around this, since the repository it's trying to use doesn't seem to work:
https://vapp-updates.vmware.com/vai-catalog/valm/vmw/8e70f769-fd50-4a7a-bee2-2c0d945e23b0/5.5.0.5100.latest








These systems still work great for many even 9+ years later, mine included, even with (unsupported) vSphere 8 and Windows 11 Version 21H2. But unless you added the optional TPM module, it may be the end of the line as far as repurposing them for running the latest Windows 11 Version 24H2 and beyond.