We present elastic and inelastic spin-changing cross sections for cold and ultracold NH(X 3Σ−) + NH(X 3Σ−) collisions, obtained from full quantum scattering calculations on an accurate ab initio quintet potential-energy surface. Although we consider only collisions in zero field, we focus on the cross sections relevant for magnetic trapping experiments. It is shown that evaporative cooling of both fermionic 14NH and bosonic 15NH is likely to be successful for hyperfine states that allow s-wave collisions. The calculated cross sections are very sensitive to the details of the interaction potential, due to the presence of (quasi)bound state resonances. The remaining inaccuracy of the ab initio potential-energy surface therefore gives rise to an uncertainty in the numerical cross-section values. However, based on a sampling of the uncertainty range of the ab initio calculations, we conclude that the exact potential is likely to be such that the elastic-to-inelastic cross-section ratio is sufficiently large to achieve efficient evaporative cooling. This likelihood is only weakly dependent on the size of the channel basis set used in the scattering calculations.