$\begin{array} { l }\frac{ 5 }{ x }=\frac{ 8 }{ 9 },& x≠0\end{array}$
$45=8x$
$8x=45$
$\begin{array} { l }x=\frac{ 45 }{ 8 },& x≠0\end{array}$
$\begin{align*}&x=\frac{ 45 }{ 8 } \\&\begin{array} { l }x=5 \frac{ 5 }{ 8 },& x=5.625\end{array}\end{align*}$