5. Multiply the consecutive natural numbers from 1 to 25, which is $1 \times 2 \times 3 \times \ldots \times 25$, denoted as 25! (read as 25 factorial). When 25! is divided by 3, it is clear that 25! is divisible by 3, resulting in a quotient: then divide this quotient by 3, ..., and continue dividing by 3 until the quotient is no longer divisible by 3. In this process, 3 divides 25! a total of times.
$10$