H.P. with (a_1=-\dfrac{1}{3}), (a_5=\dfrac{1}{5})

Reciprocals A.P.: (A_1=-3), (A_5=5)

[ -3+4d=5\implies 4d=8\implies d=2 ]

9th reciprocal: (-3+8\cdot2=13)

9th term of H.P.: (\dfrac{1}{13})

Answer: (\dfrac{1}{13})