High-Reynolds number separated flows involve large-scale unsteady motion which require scale-resolving computational fluid dynamics (CFD) simulations in order to provide accurate predictions. Higher-order methods have been shown to be more efficient for simulations requiring high spatial and temporal resolution, allowing for solutions with fewer degrees of freedom and lower computational cost than traditional second-order CFD methods. A higher-order space-time discontinuous-Galerkin(DG) method is presented for the scale-resolving simulation of high-Reynolds number compressible flows. The space-time DG method is implemented efficiently using a tensor-product formulation and solved with a Jacobian-free Newton-Krylov scheme and tensor-product based preconditioners. The effect of the discrete formulation on the nonlinear stability of the scheme is assessed through numerical simulations. With increasing Reynolds number, it is shown that an entropy-stable formulation is required in order to maintain stability at high-order. Using an entropy variable formulation consistent with established entropy stability theory ensures nonlinear stability at high and infinite Reynolds number. Numerical results are presented demonstrating the success of the method on a variety of subsonic compressible flows.