Use implicit differentiation to find $d y / d x$. Then find the slope of the curve at the given point. \[ 5 x y-8 x+y=40 ; \quad\left(-4,-\frac{8}{19}\right) \] \[ \frac{d y}{d x}=\frac{8-5 y}{5 x+1} \] The slope of the curve at $\left(-4,-\frac{8}{19}\right)$ is $\square$.

Step 1 ：Use implicit differentiation to find \(\frac{d y}{d x}\).

Step 2 ：\(\frac{d y}{d x}=\frac{8-5 y}{5 x+1}\)

Step 3 ：Substitute the x and y coordinates of the given point into the derivative to find the slope at that point.

Step 4 ：\(\frac{d y}{d x} = \frac{8 - 5*(-\frac{8}{19})}{5*(-4) + 1}\)

Step 5 ：Simplify the expression to find the slope.

Step 6 ：The slope of the curve at \(\left(-4,-\frac{8}{19}\right)\) is \(-0.531855955678670\).

Step 7 ：Final Answer: The slope of the curve at \(\left(-4,-\frac{8}{19}\right)\) is \(\boxed{-0.531855955678670}\).