The magician and the five cards

1. Among five cards there are always at least two of the same suit.
2. One can be hidden and another revealed to set the suit of the secret card.
3. With the remaining three you do not indicate the exact value directly: you encode a distance within that suit.

Yes, you always can. The idea has two layers. First: among 5 cards there are always at least 2 of the same suit. So the wizard can choose one of those two to hide and another to show first. With that, the magician now knows the suit of the secret card. Second: within the same suit, if we cycle through the values
A, 2, 3,..., 10, J, Q, K, A,
Between two cards you can always choose a direction whose distance is 1, 2, 3, 4, 5 or 6. The wizard decides which of the two to hide and which to show so that the coded distance is one of those six. There are then 3 cards left to sort. And 3 cards can be ordered from

$$ 3! = 6 $$

different ways. So, the wizard uses:

• the first card shown to set the suit;
• the order of the other three to code the distance 1–6 within that suit. The magician sees the base card, reads the distance from the order of the remaining three, advances that number of steps within the same suit, and retrieves the exact hidden card.