5. Multiply the consecutive natural numbers from 1 to 25, which is $1 \times 2 \times 3 \times \cdots \times 25$, 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, ..., continue dividing by 3 until the quotient is no longer divisible by 3. In this process, 3 divides $\qquad$ times.
Equivalent to calculating how many factors of 3 are in 25!;
Multiples of 3: $[25 \div 3]=8$ (numbers), multiples of 9: $[8 \div 3]=2$ (numbers)
Total factors of 3: $8+2=10$ (numbers), so 3 divides exactly 10 times.