3♣ was fourth-suit forcing, one of the few conventions that are allowed. 5♠ was a general invitation - "bid six if you think you have a suitable hand".
[1] Criticise the bidding, bearing in mind that if South's king of diamonds was the king of hearts the slam would be very good, but also bearing in mind that the poor fellow probably thought his ♦K was a good card anyway given his partner's 2♦ response.
[2] More importantly, plan the play on the opening lead of ♥K.
[3] If you complete [2] successfully, you will make the contract. Conjecture why this might have been very unlucky.