We need to convert this equation to slope-intercept form first.
We can do that by solving for y.
x - 5y = 15
Add 5y to both sides.
x = 5y + 15
Subtract 15 from both sides.
x - 15 = 5y
Divide both sides by 5.
y = 1/5x - 3
We now know the slope is 1/5.
The slope of the line perpendicular to the line with a slope of 1/5 is -5.
The slope of a perpendicular line is the negative reciprocal of the original slope.
Using a graphing calculator, we know the y-intercept of the line that is perpendicular to the original line must have a y-intercept of -6 to run through the points (-2, 5).
The equation of the new line is y = -5x - 6.
