To calculate the slope of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]
For the points \((-4, 5)\) and \((8, -1)\), we can identify:
\[ (x_1, y_1) = (-4, 5) \quad \text{and} \quad (x_2, y_2) = (8, -1) \]
Now, we can substitute these values into the slope formula:
\[ \text{slope} = \frac{-1 - 5}{8 - (-4)} \]
Calculating the differences:
\[ \text{slope} = \frac{-6}{8 + 4} = \frac{-6}{12} \]
Now, we simplify the fraction:
\[ \text{slope} = \frac{-1}{2} \]
Thus, the slope of the line is:
\[ \boxed{-\frac{1}{2}} \]