Here are the instructions. Then we'll do your specific problem.
Step 1: Solve the equation for y, and write it in the form y = mx + b.
Step 2: The slope is m, and the y-intercept is b.
Now let's start.
-2x - 5y = -20
To solve for y, we first add 2x to both sides.
-5y = 2x - 20
Now we divide both sides by -5.

Now we compare what we got with the form, y = mx + b.
We see that m = -2/5, and b = 4. m is the slope, and b is the y-intercept.
slope: -2/5
y-intercept: 4