The slope of the line [tex]y=5x+2[/tex] is 5. Any line perpendicular to this would have slope [tex]-\dfrac15[/tex]. 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.
[tex]y-(-3)=-\dfrac15(x-(-10))\implies y+3=-\dfrac15x-2\implies y=-\dfrac15x-5[/tex]
