Mr. S, Mr. P and Mr. Q know that there are 16 playing cards in the desk drawer: hearts A and Q. ...

There is nothing wrong with the answer. That's how I deduced it.

The first reasoning: Mr. P doesn't know, but he knows that the points of this card must overlap, so we can find out A.Q.4.5

The second reasoning: Mr. Q knows Mr. P doesn't, that is to say, there are no cards in this suit that can be identified by numbers alone, only hearts and diamonds.

The third reasoning: Mr. P knows the suit because Mr. Q knows the number, and he can recognize the card at once. It won't be a. If it is two colors of A, Mr. P can only say that he doesn't know.

The fourth sentence of reasoning: Mr. Q saw Mr. P and understood. And I know it won't be a. If Q only knows diamonds. There are only two cards in a square, so it can only be a square 5. So he also knows. If the suit that Q knows is a red heart, then Mr. Q can only say that he doesn't know.

The reasoning is over. Although Mr. S doesn't know the color and the number of points, the answer is box 5 through their reasoning dialogue.