The line perpendicular to 5x+10y = 7  has an equation  


    10x-5y = c,     (1)


where "c" is some constant, whose value is unknown right now and should be determined from the fact,

that the point (-5,2) belongs to the line (1).


For it, substitute the coordinate values of the point  x= -5,  y= 2 into equation (1).


You will get

    10*(-5) - 5*2 = c = -50 - 10 = -60.


Thus your equation is

    10x - 5y = -60,  or, equivalently,


    2x  -  y = -12.               ANSWER