Found out the hard way that you can’t use the web interface of VMware 5.5 on the free ESXi server. You need the vCenter appliance, which needs a license.
If you don’t have a PC available, you can download VirtualBox and an appliance / pre-configured VM from Microsoft (of all places).
You’ll then be able to install the vSphere client to manage your ESXi instance.
By the way, you can use VMware Workstation 10 to connect to the ESXi instance if you need to use the new features of 5.5.
Not exactly a fantastic solution. A valid workaround, at least. One step closer to justifying the move to KVM…