Answer
$$\frac{\partial w}{\partial x}-5 \frac{\partial w}{\partial y}=0$$
Work Step by Step
Given $$w=f(s),\ \ \ \ \ s= y+5x$$
Since
\begin{align*}
\frac{\partial w}{\partial x}&=\frac{\partial w}{\partial s}\frac{\partial s}{\partial x}= 5\frac{\partial w}{\partial s}\\
\frac{\partial w}{\partial y}&=\frac{\partial w}{\partial s}\frac{\partial s}{\partial y}=\frac{\partial w}{\partial s}
\end{align*}
Then
\begin{align*}
\frac{\partial w}{\partial x}-5 \frac{\partial w}{\partial y}&= 5\frac{\partial w}{\partial s}-5\frac{\partial w}{\partial s}\\
&=0
\end{align*}
