$$X \sim B(n, p)$$
$$P(X=2)= \frac{80}{243} \quad \quad \quad P(X=5)= \frac{12}{729}$$
Find $n$ and $p$.
Why is $n=6$ and $p=\frac{1}{3}$? We cannot use simultaneous equations. However, I think its something to do with $243 = 3^5$ but I am not too sure.
I don't think there is a unique solution of (n,p). put n equal to a any integer greater than 5, you will find a particular p as a solution.