\(\dfrac{x}{2}=\dfrac{y}{3};\dfrac{y}{4}=\dfrac{z}{5}\\ \Rightarrow\dfrac{x}{8}=\dfrac{y}{12}=\dfrac{z}{15}=\dfrac{x-y-z}{8-12-15}=-\dfrac{28}{19}\\ \Rightarrow\left\{{}\begin{matrix}x=\dfrac{-224}{19}\\y=\dfrac{-336}{19}\\z=\dfrac{-420}{19}\end{matrix}\right.\)