Just installed the hypervisor and it is up and running fine (in Test mode). Using the corresponding version of vSphere Client works fine too. Now sites like this show a Web Client that I just cannot see. When I visit https://my-esxi5/, the vSphere Welcome Screen does not show the Web Client link at the right side. Also, https://my-esxi5:9443/ seems to not be an open port.
Is it available at all in the free version?
No, it is not. Link to the feature faq.
I ended up using Proxmox VE. It is much more bare bones than a proper vSphere installation and in the free (as in freedom - not as in beer like ESXi) version it does not offer the fuzzy feeling of help from support if ever needed. (Not that I am a believer in a fully supported stack at all...)
But it does run fully virtualized Windows VMs (KVM) alongside Container virtualized Linuxes (OpenVZ), is completely adminstrable from a web browser, capable of forming clusters, doing live migrations and snapshot backups.
The right tool for the (my simple) job.