Brief idea of the solution
(a)
Slope of L2= -1/Slope of L1 = -1/(-2/5)
Equation of L2: (y-2)/(x-5) = Slope of L2
(b)
Put x=0 to L2 to obtain the coordinates of B (y-intercept of L2)
Let P=(a,b)
Slope of PA * Slope of PB = -1
Simplify the equation to obtain the locus of P