Find the expansions of $(a+b)^{3}$ and $(a+b)^{4}$, and provide that of $(a+b)^{5}$.
It is enough to use the correct line of Pascal's triangle. For $n=5$, we have

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