  By calculating the second-order pole in the operator product expansion (OPE)
between the spin-3 Casimir operator and the spin-4 Casimir operator known
previously, the spin-5 Casimir operator is obtained in the coset model based on
(A_{N-1}^{(1)} \oplus A_{N-1}^{(1)}, A_{N-1}^{(1)}) at level (k,1). This spin-5
Casimir operator consisted of the quintic, quartic (with one derivative) and
cubic (with two derivatives) WZW currents contracted with SU(N) invariant
tensors. The three-point functions with two scalars for all values of 't Hooft
coupling in the large N limit were obtained by analyzing the zero-mode
eigenvalue equations carefully. These three-point functions were dual to those
in AdS_3 higher spin gravity theory with matter. Furthermore, the exact
three-point functions that hold for any finite N and k are obtained. The zero
mode eigenvalue equations for the spin-5 current in CFT coincided with those of
the spin-5 field in asymptotic symmetry algebra of the higher spin theory on
the AdS_3. This paper also describes the structure constant appearing in the
spin-4 Casimir operator from the OPE between the spin-3 Casimir operator and
itself for N=4, 5 in the more general coset minimal model with two arbitrary
levels (k_1, k_2).
