We present new radio/millimeter measurements of the hot magnetic star HR 5907 obtained with the VLA and ALMA interferometers. We find that HR 5907 is the most radio luminous early type star in the cm–mm band among those presently known. Its multi-wavelength radio light curves are strongly variable with an amplitude that increases with radio frequency. The radio emission can be explained by the populations of the non-thermal electrons accelerated in the current sheets on the outer border of the magnetosphere of this fast-rotating magnetic star. We classify HR 5907 as another member of the growing class of strongly magnetic fast-rotating hot stars where the gyro-synchrotron emission mechanism efficiently operates in their magnetospheres. The new radio observations of HR 5907 are combined with archival X-ray data to study the physical condition of its magnetosphere. The X-ray spectra of HR 5907 show tentative evidence for the presence of non-thermal spectral component. We suggest that non-thermal X-rays originate a stellar X-ray aurora due to streams of non-thermal electrons impacting on the stellar surface. Taking advantage of the relation between the spectral indices of the X-ray power-law spectrum and the non-thermal electron energy distributions, we perform 3-D modelling of the radio emission for HR 5907. The wavelength-dependent radio light curves probe magnetospheric layers at different heights above the stellar surface. A detailed comparison between simulated and observed radio light curves leads us to conclude that the stellar magnetic field of HR 5907 is likely non-dipolar, providing further indirect evidence of the complex magnetic field topology of HR 5907.