Question seems complicated, but is not.
But let point A be (-3,b). The given line has gradient -(2/5). Therefore gradient of AB is 5/2.
Since B is (3,5), gradient of AB being (5-b)/(3+3) = 5/2. It follows b = -10
i.e the required point A is (-3,-10)
Silove's solution rather long-winded and is harder than necessary. You don't need the equation of AB.