We recently developed an adiabatic theory for cold molecular collision experiments. In our previous application of this theory (Pawlak, M.; et al. J. Chem. Phys. 2015, 143, 074114), we assumed that during the experiment the collision of an atom with a diatom takes place when the diatom is in the ground rotational state and is located in a plane. In this paper, we present how the variational approach of the adiabatic theory for low-temperature collision experiments can be used for the study a 5D collision between the atom and the diatomic molecule with no limitations on its rotational quantum states and no plane restrictions. Moreover, we show here the dramatic differences in the measured reaction rates of He(2(3)S(1)) + ortho/para-H2 -> He(1s(2)) + ortho/para-HI2+ + e(-) resulting from the anisotropic long-range interactions in the reaction. In collisions of metastable helium with molecular hydrogen in the ground rotational state, the isotropic potential term dominates the dynamics. When the collision is with molecular hydrogen in the first excited rotational state, the nonisotropic interactions play an important role in the dynamics. The agreement of our results with the latest experimental findings (Klein, A.; et al. Nat. Phys. 2017, 13, 35-38) is very good.