Hello swiss_member, 5.1 audio is supported via HDMI (attention, make sure that your HDMI cable also transmits audio data) or TosLink. In my case, unfortunately, it does not switch automatically, but a small remote control is included with which you can switch the sources.

The audio output is limited to the audio formats that the display supports. In the HDMI handshake, the source asks the display which formats are supported, and then decides which signal to send. The switch has no influence on the handshake, and from the audio output you only get what is sent from the source.
This means for example if you have a projector as output, and it only supports stereo, the source only sends PCM stereo (because in any case the projector could not decode DTS/DD etc.) and you only get stereo from the optical output of the switch.
If you have a current TV as output that can decode 5.1, you should get 5.1 from the Switch.
Hope it is clear...