When you're graphing a line in slope-intercept form (y = mx + b), your first step is to look at b, which is your y-intercept. The y-intercept is where your line touches the y-axis.
Slope-intercept form is y = mx + b, but for y = -5x doesn't have a b, so you have to add one. You can do this by adding + 0 to the end, since it won't change your equation.
y = -5x + 0
b = y-intercept = 0
m = slope = -5
So, your line will start at 0 on the y-intercept, which will be at the origin point (0,0).
Your slope is -5, or , so you'll go down 5 and then to the right 1.
A few points on your line should be (0,0), (1,-5), and (-1,5).