5. Place 3 balls, red, yellow, and blue, randomly into 5 different boxes $A, B, C, D, E$. The probability that exactly two balls are placed in the same box is $\qquad$ .
Answer: $\frac{12}{25}$.
Solution: The sample space contains $5^{3}=125$ elements. The number of elements that satisfy the condition of exactly two balls being placed in the same box is $C_{3}^{2} \times P_{5}^{2}=60$. Therefore, the required probability is $p=\frac{60}{125}=\frac{12}{25}$.