The OPERA experiment was designed to search for $\nu_{\mu} \rightarrow \nu_{\tau}$ 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 $\nu_{\mu} \rightarrow \nu_{\tau}$ appearance, achieved with four candidate events in a sub-sample of the data, was previously reported. In this paper, 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 assessing the discovery of $\nu_{\mu}\rightarrow \nu_{\tau}$ oscillations in appearance mode with a significance larger than 5 $\sigma$.
