The hydrodynamically evolved elliptic flow of charged hadrons is studied through multiparticle correlations in PbPb collisions at $\sqrt{s_{NN}} = 5.02$ TeV, corresponding to an integrated luminosity of $0.607
nb^{-1}$. $v_{2}\{2k\}$ are measured up to the tenth order (k = 5) as functions of the collision centrality. They are shown to follow the ordering : $v_{2}\{2\} > v_{2}\{4\} \gtrsim v_{2}\{6\} \gtrsim v_{2}\{8\} \gtrsim v_{2}\{10\}$. The centrality-dependent moments - skewness, kurtosis and, for the first time, superskewness, are measured for the fluctuation-driven event-by-event $v_{2}$ distribution. These moments can be good probes of the initial-state geometry in high-energy nucleus-nucleus collisions, assuming a hydrodynamic expansion.