The OPERA experiment was designed to search for nu(mu) -> nu(tau) oscillations in appearance mode, i.e., by detecting the tau leptons produced in charged current nu(tau) interactions. The experiment took data from 2008 to 2012 in the CERN Neutrinos to Gran Sasso beam. The observation of the nu(mu) -> nu(tau) appearance, achieved with four candidate events in a subsample of the data, was previously reported. In this Letter, a fifth nu(tau) candidate event, found in an enlarged data sample, is described. Together with a further reduction of the expected background, the candidate events detected so far allow us to assess the discovery of nu(mu) -> nu(tau) oscillations in appearance mode with a significance larger than 5 sigma.