5. For several identical books, 104 rubles were paid. The price of one book is a natural number. How much does one book cost if more than 10 but less than 60 were bought?
5. 6) $104: 10=10$ (remainder 4) (rubles) - the price of one book if there were 10 books;
2) $104: 60=1$ (remainder 44) (rubles) - the price of one book if there were 60 books.

Therefore, the price of one book is more than 1 ruble but less than 10 rubles. Thus, the price of one book can be 2, 3, 4, 5, 6, 7, 8, or 9 rubles.

The number 104 is not divisible by 5, 6, 7, or 9. Therefore, the price of one book can be 2, 4, or 8 rubles.

We can find the solution by considering the factors of the number 104:

\[
\begin{aligned}
& 104=1 \times 104 \\
& 104=2 \times 52 \\
& 104=4 \times 26 \\
& 104=8 \times 13
\end{aligned}
\]

$1 \times 104$ does not satisfy the condition that the number of books is more than 10 but less than 60. The numbers 13, 26, and 52 do satisfy this condition. Therefore, the price of the books could be 2, 4, or 8 rubles.

Answer: One book can cost 2 rubles, 4 rubles, or 8 rubles.