Simulations of Mach 5 turbulent flow over a twenty-eight degree compression corner are performed using a hybrid large-eddy / Reynolds-averaged Navier-Stokes (LES/RANS) method. The model captures the mean-flow structure of the interaction reasonably well, with observed deficiencies relating to an under-prediction of the displacement effects of the shock-induced separation region. The computational results provide some support for a recent theory concerning the underlying causes of low-frequency shock wave oscillation. In the simulations, the sustained presence of a collection of streaks of fluid with lower / higher momentum than the average induces a low-frequency undulation of the separation front. Power spectra obtained at different streamwise stations are in good agreement with experimental results, indicating that the hybrid LES/RANS model is capable of predicting both low- and high-frequency dynamics of the interaction. Downstream of re-attachment, the simulations capture a three-dimensional mean-flow structure, dominated by counter-rotating vortices that produce wide variations in the surface skin friction. Predictions of the structure of the re-attaching boundary layer agree well with experimental Pitot pressure measurements. In comparison with Reynolds-averaged model predictions, the hybrid LES/RANS model predicts more amplification of the Reynolds stresses and a broadening of the Reynolds stress distribution within the boundary layer that is probably due to reattachment shock motion.