To find the slope of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula for the slope \(m\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Given the points \((-10, -1)\) and \((5, -4)\), we can assign:
- \(x_1 = -10\)
- \(y_1 = -1\)
- \(x_2 = 5\)
- \(y_2 = -4\)
Now, we can substitute these values into the slope formula:
\[ m = \frac{-4 - (-1)}{5 - (-10)} \]
Simplifying this:
\[ m = \frac{-4 + 1}{5 + 10} = \frac{-3}{15} \]
Now, simplify \(\frac{-3}{15}\):
\[ m = \frac{-1}{5} \]
Thus, the slope of the line that passes through the points \((-10, -1)\) and \((5, -4)\) is \(\boxed{-\frac{1}{5}}\).