Answer
$-243i$
Work Step by Step
Here, we are using the pattern of squaring i.
For example, $i^{1}=i$, $i^{2}=-1$, $i^{3}=-1\times i=-i$, $i^{4}=-i\times i=-i^{2}=-1\times-1=1$, and so on.
Therefore, we can use the fact that $i^{4}=1$ and then rewrite the expression in terms of $i^{4}$ in order to simplify.
$(-3i)^{5}=(-3)^{5}i^{5}=-243(i^{4}\times i)=-243(1\times i)=-243(i)=-243i$