At this point, the two auctions diverge.
In auction 1, you're playing Fantunes, so with your opening 1♠ you already showed a hand about a king stronger than a normal opening. Over 5♥, partner makes a forcing pass, and you X to show a min (agree?). He now rebids 5♠, showing some slam interest. What's your call?
In auction 2, you're playing regular 2/1, so your opening 1♠ showed about a king less, and partner's GF 2♣ showed about a commensurate king more than in auction 1. Over 5♥, P now just bids 5♠. What's your call now?