  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 $\sigma$.
