The influence of non-equilibrium kinetic processes on macroscopic parameters in air flows is a challenging and an important problem. Particularly, simulation of flows with high-temperature effects is important near the surface of spacecraft or meteorites when they enter the Earth's atmosphere. Non-equilibrium flows of a reacting five-component air mixture consisting of N₂, O₂, NO, N, O behind a shock wave at different altitudes in the Earth's atmosphere and different speeds of the inlet flow are investigated. The lengths of the relaxation zones are considered to evaluate the applicability of one-temperature thermodynamics model for calculating the macroscopic fluid quantities behind the shock wave. The results of the flow simulation are obtained with in-house code developed for super- and hypersonic applications. The results from the code are compared with the results of numerical calculations computed with the equilibrium thermodynamics model.