Auroral radio emissions reveal physics of beam-plasma interactions and provide possibilities to remotely sense ionospheric plasma processes.Sato et al. (2012) recently discovered that auroral roar emissions, long known to occur at two and three times the electron gyrofrequency (fce), also occur at 4fce. Using data from wave receivers in the British Antarctic Survey Automatic Geophysical Observatories, we confirm the existence of 4fce-roars and observe for the first time 5fce-roars. A search at higher frequencies did not find higher harmonics. Both 4fce- and 5fce-roars only occur in sunlit conditions near summer solstice. Harmonic roar emission frequencies scale with the strength of the geomagnetic field, and combining data from four observatories suggests that the 4fce-roar source height lies around 245 km, lower than the 275 km estimated for 2fce-roar. These observations show that the auroral roar generation mechanism acts under a broader set of plasma conditions than previously considered.