A potential energy surface for H5+ has been constructed by a modified Shepard interpolation on a sparse set of data points, using second order Möller–Plesset perturbation theory. An improved version of the surface was also obtained by substituting the energy values at the data points with values evaluated using a coupled cluster treatment (with single and double excitations, and perturbative treatment of triple excitations). Classical simulations for the collisions between H3++HD and H3++D2 were carried out in order to calculate the total integral cross sections and rate coefficients for these systems. There is good agreement with earlier experimental data for rate coefficients at temperatures between 80 and 300 K, but the predicted rate coefficient for the reaction of H3++HD at 10 K deviates from the most recent experimental measurement, suggesting that quantum rather than classical reaction dynamics are necessary.