5. Ana rolled a die three times and in each roll, she got a natural number from 1 to 6. She told Peter the product of those three (not necessarily distinct) numbers, and told Zoran the sum (both of them knew what the communicated values represented). The following conversation took place between Peter and Zoran:

- Peter: "I cannot determine with certainty all three numbers that Ana got."
- Zoran: "I knew you couldn't."
- Peter: "Although I didn't know even the smallest number that Ana got so far, thanks to your comment, I now know."

What are the three numbers (in some permutation) that Ana got?
5. Let's note that for all possible sums except 6, there is a combination of three numbers with that sum such that it is possible to uniquely reconstruct those three numbers based on their product: $18=6+6+6, 17=6+6+5, 16=6+5+5, 15=5+5+5, 14=5+5+4, 13=5+5+3, 12=5+5+2, 11=5+5+1$, $10=4+4+2, 9=3+3+3, 8=5+2+1, 7=5+1+1, 5=3+1+1, 4=2+1+1$, and $3=1+1+1$. For example, if Zoran had been told the sum 14, then one way to get that sum is $5+5+4$, and in that case, Petar would have been told the product 100, and in that case, Petar would immediately know all three of Ana's numbers (the only way to represent 100 as the product of three natural numbers from 1 to 6 is indeed $5 \cdot 5 \cdot 4$: since $5^2 \mid 100$, it follows that two of those three numbers must be 5, and the third must be 4). Since Zoran was sure that Petar could not reconstruct Ana's numbers based on his product, the only way Zoran could be sure of this is if he was told the sum 6.

This means that Ana received one of the following three sets of numbers: $(4,1,1)$, $(3,2,1)$, or $(2,2,2)$. In the first case, Petar would have the product 4 and would be uncertain between the sets $(4,1,1)$ and $(2,2,1)$; in the second case, Petar would have the product 6 and would be uncertain between the sets $(3,2,1)$ and $(6,1,1)$; in the third case, Petar would have the product 8 and would be uncertain between the sets $(4,2,1)$ and $(2,2,2)$. Since Petar stated that he did not know which was the smallest of Ana's numbers, the first two cases are eliminated, leaving the third. Therefore, Ana rolled the number 2 each time in the three rolls.