#### Answer

$i$

#### Work Step by Step

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