We have:

\(\dfrac{x}{5}\) = \(\dfrac{y}{2}\) = \(\dfrac{z}{3}\) = \(\dfrac{2x-3y+5z}{10-6+15}\) = \(\dfrac{38}{19}\) = \(2\)

\(\dfrac{x}{5}\) = \(2 => x = 10 \)

\(\dfrac{y}{2}\) = \(2 => y = 4\)

\(\dfrac{z}{3}\) = \(2 => z = 6\)