#### Answer

$-243i$

#### Work Step by Step

Using $i^2=-1$ and the laws of exponents, the given expression, $
(-3i)^{5}
,$ is equivalent to
\begin{array}{l}\require{cancel}
(-3)^5i^5
\\\\=
-243i^5
\\\\=
-243i^4\cdot i
\\\\=
-243(i^2)^2\cdot i
\\\\=
-243(-1)^2\cdot i
\\\\=
-243(1)\cdot i
\\\\=
-243i
\end{array}