License key does not work

I got the free license key for Rhino for Mac. (I’m sure I got it in the Rhino 6 for Mac Evaluation) When I try to open Rhino and enter this licence key Rhino says: ‘The Rhino for Windows license key you entered is not valid in Rhino for Mac.’

I downloaded an older version of Rhino for mac (5.5.3) because I don’t want to update my Mac to macOS High Sierra 10.13.6. Can this be the problem?

Yes, it is exactly the problem. You cannot run Rhino V5 with a V6 license key. Unfortunately, V5 is no longer available as an evaluation version.