Put simply, this question is asking the probability of having rain atleast twice in the next 5 days. The easiest way that comes to mind is reverse count - find the probability of it not happening. There are two cases for this:
Raining only once:
This has a .7^4 * 0.3 * 5 chance
Raining no times:
This has a .7^5 chance
Adding these together you get 0.52822
This is the inverse probability, so to find the actual probability, subtract it from 1.
