I just realised that part of why we've been getting 5e questions tagged dungeons-and-dragons instead of dnd-5e is because someone typing in "dungeo…" isn't going to see the 5e tag pop up.
I would do it, but you can't propose a non-existent tag as a synonym. (And I don't want to abuse some poor question with an arbitrary edit just to make the tag exist long enough for synonym voting…)
Could a mod create dungeons-and-dragons-5e as a synonym of dnd-5e?
We'll still get people mistagging with dungeons-and-dragons when they mean dnd-5e, but this should cut it down somewhat.