\(\dfrac{x}{5}=\dfrac{y}{2}=\dfrac{z}{-3}=k\)
\(\Rightarrow xyz=5.2.\left(-3\right).k=-30k=240\Rightarrow k=-8\)
\(\Rightarrow\left\{{}\begin{matrix}x=\left(-8\right).5=-40\\y=\left(-8\right).2=-16\\z=\left(-8\right).\left(-3\right)=24\end{matrix}\right.\)