Transition of a Mach 5.65 laminar boundary layer tripped by an array of diamond-shaped roughness elements with the trip-spacing ratio of s/D = 3 (s is the spanwise trip-spacing, and D is the spanwise trip-width) is studied using large-scale direct numerical simulations. No forcing other than the roughness elements is used to trip the boundary layer. In order to accurately capture high-frequency coherent structures, a high-order, low-dissipation scheme for the convection terms in the Navier-Stokes equations is used. Three dominant and dynamically significant flow structures are observed: the upstream vortex system, the shock system, and the downstream separated shear layers/counter-rotating streamwise vortices which originate from the top and sides of the roughness elements. A peak-amplitude frequency at St = 0.11 (consistent to s/D = 2) is observed in the upstream and downstream locations using the PSD of pressure fluctuations. Furthermore, the source of the transition mechanism is also consistently found to be the interaction between the shear layers from the top edges and corners of each tripping element, and the counter-rotating streamwise vortices from its wake region. This interaction roughness the shear layers to roll-over on top of the streamwise vortices to form hairpin-like structures. These hairpin-like structures subsequently breakdown to turbulent flow. However, due to the larger trip-spacing in the present case (s/D = 3), the interaction occurs further downstream (compared to that in the case of s/D = 2) delaying flow breakdown.