Display manager to login to virtual machine
 

Is it possible that a user logs in to a desktop that is provided by a virtual machine on the host.

I want to achieve that a certain user gets a desktop of a runlevel 5 virtual machine that resides on the same host...

I'm sure it is possible - I don't mess around with virtual machines at all, but if you could somehow specify which VM to run when you call the VM application you are using (VirtualBox, VMWare,...), you could just list that command in the user's ~/.xinitrc file, and all should be good!