5. Four different digits are written on two cards - one on each side of the card. Can it be that every two-digit number that can be formed from these cards is prime? (Digits cannot be flipped upside down, i.e., you cannot turn a 6 into a 9 or vice versa.)

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# Solution:

All two-digit numbers ending in $0, 2, 4, 6$ or 8 are even, and those ending in 5 are multiples of five. Therefore, such numbers cannot be prime, and it makes no sense to write these digits on the cards. The remaining digits are 1, 3, 7, and 9. If the digits 3 and 9 are written on different cards, then they can form the composite number 39. If they are written on the same card, then 1 and 7 are written on the other card, and then the composite number $91=7 \cdot 13$ can be formed.

Answer: No.

Comment. It is proven that the digits $0, 2, 4, 6, 8, 5$ are not written on the cards - 2 points.