To find the slope of the line given by the equation \( y - 10 = -5(x + 20) \), we will rewrite the equation in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope.
Starting with the equation:
\[ y - 10 = -5(x + 20) \]
First, distribute \(-5\):
\[ y - 10 = -5x - 100 \]
Next, add \(10\) to both sides:
\[ y = -5x - 100 + 10 \]
This simplifies to:
\[ y = -5x - 90 \]
Now, we can see that the slope \( m \) is \(-5\).
So the slope of the line is:
\[ \boxed{-5} \]