Aims: The aim of the project is to improve our current knowledge of the density of T dwarfs and the shape of the substellar initial mass function by identifying a magnitude-limited sample of T dwarfs in the full southern sky. Methods: We present the results of a photometric search aimed at discovering cool brown dwarfs in the southern sky imaged at infrared wavelengths by the Visible and Infrared Survey Telescope for Astronomy (VISTA) and the Wide Infrared Survey Explorer (WISE) satellite mission. We combined the first data release (DR1) of the VISTA Hemisphere Survey (VHS) and the WISE preliminary data release to extract candidates with red mid-infrared colours and near- to mid-infrared colours characteristics of cool brown dwarfs. Results: The VHS DR1 vs. WISE search returned tens of T dwarf candidates, 13 of which are presented here, including two previously published in the literature and five new ones confirmed spectroscopically with spectral types between T4.5 and T8. We estimate that the two T6 dwarfs lie within 16 pc and the T4.5 within 25 pc. The remaining three are 30-50 pc distant. The only T7 dwarf in our sample is the faintest of its spectral class with J = 19.28 mag. The other six T dwarf candidates remain without spectroscopic follow-up. We also improve our knowledge on the proper motion accuracy for three bright T dwarfs by combining multi-epoch data from public databases (DENIS, 2MASS, VHS, WISE, Spitzer). Based on observations made with the Calar Alto 3.5-m telescope, the Magellan telescope at Las Campanas, the ESO Very Large Telescope at the Paranal Observatory, and the IAC80 at Teide Observatory.Figures 1 and 2 are available in electronic form at http://www.aanda.org