Direct Numerical Simulations (DNS) were carried out in order to investigate laminar-turbulent boundary-layer transition for a sharp 7◦ half-angle straight (right) cone with a sharp nose tip at Mach 5 and zero angle of attack. The cone geometry and flow conditions of the experiments in the Hypersonic Wind Tunnel 5 (HWT-5) at Sandia National Laboratories were used for the numerical investigations. Results of three-dimensional pulse simulations indicate that a so-called fundamental and a so-called “oblique breakdown” scenario are possible relevant nonlinear transition mechanisms for the investigated geometry and flow conditions. In addition to the “classical” breakdown scenarios the wave packet simulations also revealed the possibility of first and second mode interactions. Highly-resolved “controlled” breakdown simulations of a fundamental breakdown, an oblique breakdown and a breakdown initiated by an axisymmetric second mode with a pair of oblique first mode disturbances confirm that any of these nonlinear mechanisms can lead to transition. The DNS results indicate that the oblique breakdown and the combined first mode, second mode interaction breakdown lead to transition more rapidly (in a shorter downstream distance) compared to the fundamental breakdown.