y = mx + b is the equation of a line. m is the slope. If you have two parallel lines, they will have the same slope, so m will be the same on both of them.
In your case, you have y = -3x + 5, so m = -3
This means the parallel line will also have a slope of -3, so it's equation is y = -3x + b. You still need to solve for b. You have a point, (-2, -6), so you can just plug that in to solve for b.
y = -3x + b
-6 = -3 * -2 + b
-6 = 6 + b
Subtract 6 from both sides to get b by itself
-12 = b
So the equation of the line you are looking for is y = -3x - 12