This did not entirely work for me. My version of the launcher does not have the UE5/UE4 tabs, plus the dropdown next to 4.26 on the pic above was not there (4.27 in my case). Clicking the “+” next to engine versions did nothing for me.
This took a while to figure out, but the “top right” install button adds an engine version WITHOUT the “arrow dropdown”. Uninstall any unreal versions.
With an empty list of game versions, on the “Unreal Engine/Library” page, the “Engine Versions +” adds an engine version WITH the missing dropdown icon and can then select Unreal 5 from that dropdown.