How do I activate Screen Mirroring on a Samsung Galaxy S5 running Marshmallow?
You did not mention this in your question, but your screenshot shows that you are using the Galaxy S5 Neo.

Unfortunately, that's one of the subtle differences between the Galaxy S5 and the Galaxy S5 Neo: On the Neo, Samsung silently dropped support for the screen mirroring feature.

I could not find any official sources for this, but there seems to be consensus in the community that screen mirroring (MiraCast) is just not available on the Neo (Source 1, Source 2: German, see Community Question section). 

If you check the list of MiraCast certified devices, you will notice that the S5 (SM-G900F) is listed, but the S5 Neo (SM-903F) is not.