There have been numerous reports of the Emperor's missions not registering. Most seem to have resolved themselves after waiting for a period of time.
In any case, the Emperor's missions are not critical to completion of the game, and the payout is not very good for them. So, continue playing the game, and if it resolves, great. If not, it should not hamper your enjoyment of the game.
The Emperor's missions are merely a guide for playing the game, but if you choose to disregard the missions, you can build any levels you like.
UPDATE: I had the same mission just today. And, while I'm certain I had 5 more more bitizen move in here and there, I did not receive the credit until using a recruiting agent and having 5 move in on a new residential floor.