In order to study the magnetic properties of a mixed spin-2 and spin-5/2 ferrimagnetic Ising system on a two-dimensional honeycomb lattice, we carried out Monte Carlo simulations. We found that the system which includes only a nearest-neighbour interaction and a single-ion anisotropy just on a spin-2 does not have a compensation point. The result contradicts that predicted by the effective-field theory. The inconsistency arises from how one estimates the two-point and three-point correlations.