Extended cluster models together with density-functional theory are used to evaluate geometric, energetic, and electronic properties of different adsorbate species that can occur at a vanadium oxide surface where the selective catalytic reduction (SCR) of NO in the presence of ammonia proceeds. Here, we focus on atomic hydrogen, nitrogen, and oxygen, as well as molecular NO and NHx, x = 1, 4, adsorption at a model V2O5(010) surface. Binding sites, oxygen and vanadium, at both the perfect and reduced surface are considered where reduction is modeled by (sub-) surface oxygen vacancies. The reactants are found to bind overall more strongly at oxygen vacancy sites of the reduced surface where they stabilize in positions formerly occupied by the oxygen (substitutional adsorption) compared with weaker binding at the perfect surface. In particular, ammonia, which interacts only weakly with vanadium at the perfect surface, binds quite strongly near surface oxygen vacancies. In contrast, surface binding of the NH4 adsorbate species differs only little between the perfect and the reduced surface which is explained by the dominantly electrostatic nature of the adsorbate interaction. The theoretical results are consistent with experimental findings and confirm the importance of surface reduction for the reactant adsorption forming elementary steps of the SCR process.