5. For several identical pictures, 104 rubles were paid. How much does one picture cost if more than 10 but less than 60 were bought and the price of one picture is a natural number.
5. First method of solving. Let's factorize the number 104:

$$
104=2 \times 2 \times 2 \times 13
$$

Therefore, the cost of the pictures could be 2, 4, 8, 13, 26, 52, 104 rubles. We will exclude from these numbers those that do not satisfy the conditions that more than 10 but less than 60 were bought.

These numbers are 13, 26, 52, 104, since their product with 10 would be greater than 104. Thus, the cost of the pictures can be 2, 4, or 8 rubles.

Second method of solving. Let's determine the range in which the price of the picture lies. For this, we divide 104 by 10 and 60 with a remainder (104:10 = 10 rubles (remainder 4), 104:60 = 1 ruble (remainder 44). Therefore, the price of the picture is more than 1 ruble but less than 10 rubles. The price of the picture can be 2, 3, 4, 5, 6, 7, 8, 9 rubles. We will choose from the obtained numbers those that divide 104 without a remainder. There are three such numbers - 2, 4, 8. Answer: the price of the picture is 2, 4, or 8 rubles.