First put 5x-y=6 in y=mx+b form and you get y=5x+6 which means the slope of this line is +5. The line perpendicular will have a slope of -1/5 and contains the point (-10,-4) so the equation of the line is y=-x/5 -6
Now you can construct a righ t triangle where the distance is the hypotenuse which you can solve for by pythagorean theorem . I Will leave that for you