The slope of the line \(y=5x+2\) is 5. Any line perpendicular to this would have slope \(-\dfrac15\). Since you know a point that the perpendicular line passes through, you can use the point-slope form to find the equation of the perpendicular line.
\(y-(-3)=-\dfrac15(x-(-10))\implies y+3=-\dfrac15x-2\implies y=-\dfrac15x-5\)
