In the present paper non-equilibrium flows of CO2/CO/O2/O/C mixture behind shock waves is studied taking into account vibrational excitation of CO2, CO, O2 molecules. The kinetic scheme includes vibrational energy transitions, dissociation, recombination and exchange chemical reactions. The problem is solved in the five-temperature kinetic theory approximation. The equations for vibrational temperatures of symmetric-bending and asymmetric CO2 modes and for diatomic species are coupled to the gas dynamic equations and applied to study flow parameters in the relaxation zone behind shock waves. Different models for one-temperature and multi-temperature rates of chemical reactions are used in calculations and the influence of exchange reactions and reaction models on flow parameters in the relaxation zone behind the shock wave is studied in the paper.