High-order scheme has advantages in the simulations of complex flow for its good behavior of preserving high spatial resolution with lower cost than the second order methods. WCNS-E-5(weighted compact nonlinear scheme) was applied in the simulations of thermo-chemical nonequilibrium flow around a cylinder with the freestream velocity from 5 km/s to 5.7 km/s. The distribution of correct flow field parameter was acquired, the pressure and heat flux on the surface agreed well with the experimental data. WCNS-E-5 also exhibited better performance on the grid convergence of heat flux than the second order MUSCL scheme. Results show that the present attempt to combine high order scheme with the calculations of stiff chemically reacting flow is basically successful, and it has established a good foundation for the further study.