Mr. A's first sentence can exclude single-point cards: that is, J, 8, 2 and K, that is, Mr. A said that this point can only be one of A, Q, 4 and 5;

Mr. B's first sentence "I know you don't know this card", if A takes a single card, Mr. B's judgment may be wrong. Since Mr. B is sure, it means that Mr. B knows in advance that A can't get a single card, which means that spades and flowers are excluded; That is, Mr. X said that the color of this card is: hearts or diamonds;

Now look at this card that may be drawn:

Hearts: a, q, 4

Diamonds: a, 5

Now that Mr. A knows, the point is not A. If it is A, Mr. A can't deduce it even if he knows the color. That is, Mr. A said that this point is not A, so leave:

Hearts: q, 4

Square: 5

Finally, Mr. B also knows that the explanation can only be square. If you say it's a heart, Mr. B still doesn't know which card it is.

The final answer is: box 5.