The OPERA experiment was designed to search for ν_{μ}→ν_{τ} oscillations in appearance mode, i.e., by detecting the τ leptons produced in charged current ν_{τ} interactions. The experiment took data from 2008 to 2012 in the CERN Neutrinos to Gran Sasso beam. The observation of the ν_{μ}→ν_{τ} appearance, achieved with four candidate events in a subsample of the data, was previously reported. In this Letter, a fifth ν_{τ} 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 ν_{μ}→ν_{τ} oscillations in appearance mode with a significance larger than 5σ.