The line perpendicular to the line 2x - 5y + 5 = 0 is the line of the form

5x + 2y = c,         (1)


where "c" is some constant which must be determined from the other condition,


         OR ANY OTHER EQUATION EQUIVALENT TO eq(1).



This other condition for "c" is "the line (1) passes through the point (-2,8)."


Therefore, we can determine "c" from the equation (1) by substituting x= -2  and  y= 8 into equation (1).  By doing so, you will get


5*(-2) + 2*8 = c = -10+16 = 6.


So, the equation of the line (1) is 


5x + 2y = 6,   or


5x + 2y - 6 = 0.      (2)


Now multiply eq(2) by  (both sides).  You will get an equivalent equation 


 = 0.   (3).


Now comparing the equation (3) with the equation ax + by - 5 = 0,  

you can conclude that  a =    and  b = .