To find the slope of the line that passes through the points $(8, -6)$ and $(5, -1)$, we use the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Here, $(x_1, y_1) = (8, -6)$ and $(x_2, y_2) = (5, -1)$.

Substituting the coordinates into the slope formula:

$m = \frac{-1 - (-6)}{5 - 8}$

Simplify the expression:

$m = \frac{-1 + 6}{5 - 8} = \frac{5}{-3} = -\frac{5}{3}$

So, the slope of the line is $\boxed{-\frac{5}{3}}$.

Would you like any further details or explanations? Here are some related questions you might find helpful:

1. How do you interpret the slope of a line in real-world scenarios?
2. How do you find the equation of a line given two points?
3. What does a negative slope indicate about the direction of a line?
4. How can you verify the slope calculation by graphing the points?
5. How does the slope relate to the angle of a line with the x-axis?

Tip: Always remember that the slope of a line represents how much the y-coordinate changes for a unit change in the x-coordinate.