Think about the event. This can be done in two ways basically. Choosing 2 red or 3 red.
2 red: You can choose these in $\binom{3}{2}=3$ ways. You are left with 3 balls to choose from the other 5, there are $\binom{5}{3}=10$ ways to do this. So 30 ways in total.
3 red: You have to pick all red ones (there is only one way to do it). $\binom{5}{2}= 10$ ways to choose the rest.
Ok, now you need to count all possible ways of choosing 5 balls from a pool of 8: this is $\binom{8}{5}=56$.
So the answer is $\frac{10+30}{56}=\frac{40}{56} = 0.71 \cdots$.