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Put x = -3 and y = 5 intothe equation of the hyperbola y = a/x :
5 = a/(-3)
a = -15
Then, the equation of the hyperbola is :
y = -15/x ...... [1]

Put x = -3 and y = 5 into the equation of the straight line y = bx - 1 :
5 = b(-3) - 1
-3b = 6
b = -2
Then, the equation of the straight line is :
y = -2x -1 ...... [2]

To find the point of intersection, [1] = [2] :
-15/x = -2x - 1
2x² + x - 15 = 0
(2x - 5)(x + 3) = 0
x = 5/2 or x = -3

Put x = 5/2 into [2] :
y = -2(5/2) - 1
y = -6

Hence, coordinates of another intersecting point = (5/2, -6)