Use implicit differentiation to find $d y / d x$. Then find the slope of the curve at the given point.
\[
5 x y-8 x+y=40 ; \quad\left(-4,-\frac{8}{19}\right)
\]
\[
\frac{d y}{d x}=
\]

Step 1 ：First, we need to differentiate both sides of the equation with respect to \(x\). The left side of the equation is a product of two functions, \(5x\) and \(y\), so we need to use the product rule. The derivative of \(5xy\) with respect to \(x\) is \(5y + 5x \frac{dy}{dx}\). The derivative of \(-8x\) with respect to \(x\) is \(-8\). The derivative of \(y\) with respect to \(x\) is \(\frac{dy}{dx}\). So, the derivative of the left side of the equation is \(5y + 5x \frac{dy}{dx} - 8 + \frac{dy}{dx}\). The right side of the equation is a constant, so its derivative is 0.

Step 2 ：Setting the derivative equal to 0 gives us the equation \(5y + 5x \frac{dy}{dx} - 8 + \frac{dy}{dx} = 0\). We can simplify this to \(5x \frac{dy}{dx} + \frac{dy}{dx} = 8 - 5y\).

Step 3 ：Factoring out \(\frac{dy}{dx}\) gives us \(\frac{dy}{dx}(5x + 1) = 8 - 5y\).

Step 4 ：Solving for \(\frac{dy}{dx}\) gives us \(\frac{dy}{dx} = \frac{8 - 5y}{5x + 1}\).

Step 5 ：Substituting the given point \((-4,-\frac{8}{19})\) into the equation gives us \(\frac{dy}{dx} = \frac{8 - 5(-\frac{8}{19})}{5(-4) + 1}\).

Step 6 ：Simplifying the right side of the equation gives us \(\frac{dy}{dx} = \frac{8 + \frac{40}{19}}{-20 + 1} = \frac{8 \times 19 + 40}{-19} = \frac{112}{-19}\).

Step 7 ：So, the slope of the curve at the given point is \(\boxed{-\frac{112}{19}}\).