How is it possible for only one in five children to have brown eyes when their parents both have brown eyes?
Possible...yes of course! The answer could stop there but I guess you want to ask how likely it is.

Here is a chart of probability of a given kid to have eyes of a certain color given the parents eyes color. (Note that the second column contain probabilites and not odds contrary to what the figure is stating).



The probability that $k$ kids out of $n$ have eyes of a color which appears with probability $p$ is given by the probability mass function of the binomial distribution $\binom{n}{k} p^k (1-p)^{n-k}$

Knowing that both parents have brown eyes (even for your oldest sister):


The probability that exactly one out of 5 offsprings have brown eyes (and the others have eyes of another color) is about 0.015 (3 out of 200).
The probability that exactly 3 offsprings have blue eyes (and the others have eyes of another color) is about 0.0021 (2 out of 1000)


You might want to calculate the probability of having $k$ or more kids that have eyes of a given color (a p.value) is obtained by summing probabilities. For example, the probability that 3 or more kids (out of 5) have blue eyes is  $\binom{5}{3} 0.0625^3 (1-0.0625)^{5-3} + \binom{5}{4} 0.0625^4 (1-0.0625)^{5-4} + \binom{5}{5}  0.0625^5  (1-0.0625)^{5-5} ≈ 0.0022$

Learn more about Stats

You'll probably want to learn a bit about statistics if some things are unclear. You might want to make sure you understand the concept of p.value and its interest and make sure you understand what a binomial distribution is. You may also want to understand the concept of multiple testing to avoid falling in simple pitfalls.