The hydrodynamic flow-like behavior of charged hadrons in high-energy lead-lead collisions is studied through multiparticle correlations. The elliptic anisotropy values based on different orders of multiparticle cumulants, v2{2k}, are measured up to the tenth order (k = 5) as functions of the collision centrality at a nucleon-nucleon center-of-mass energy of sNN = 5.02 TeV. The data were recorded by the CMS experiment at the LHC and correspond to an integrated luminosity of 0.607 nb−1. A hierarchy is observed between the coefficients, with v2{2} > v2{4} ≳ v2{6} ≳ v2{8} ≳ v2{10}. Based on these results, centrality-dependent moments for the fluctuation-driven event-by-event v2 distribution are determined, including the skewness, kurtosis and, for the first time, superskewness. Assuming a hydrodynamic expansion of the produced medium, these moments directly probe the initial-state geometry in high-energy nucleus-nucleus collisions.