Develop $(a+b)^{5}$.
By looking at the fifth line of Pascal's triangle (the first line being numbered zero), applying the binomial theorem gives

$$
(a+b)^{5}=a^{5}+5 a^{4} b+10 a^{3} b^{2}+10 a^{2} b^{3}+5 a b^{4}+b^{5}
$$