We present elastic and inelastic spin-changing cross sections for cold and ultracold NH($X,^3Sigma^-$) + NH($X,^3Sigma^-$) collisions, obtained from full quantum scattering calculations on an accurate textit{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 $^{14}$NH and bosonic $^{15}$NH is likely to be successful for hyperfine states that allow for 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 textit{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 textit{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.
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