jmc

There are $\left(\genfrac{}{}{0ex}{}{5}{2}\right)=10$ ways to choose 2 of 5 questions to give a positive response to. For each choice, there is a probability of ${\left(\frac{2}{5}\right)}^2{\left(\frac{3}{5}\right)}^3$ that those 2 questions will yield a positive answer and the other 3 will not. Therefore, the total probability that exactly 2 of questions give a positve answer is $10{\left(\frac{2}{5}\right)}^2{\left(\frac{3}{5}\right)}^3=\boxed{\frac{216}{625}}$.