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, v(2){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 root s(NN) = 5.02TeV. 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 v(2){2} > v(2){4} greater than or similar to v(2){6} greater than or similar to v(2){8} greater than or similar to v(2){10}. Based on these results, centrality-dependent moments for the fluctuation-driven event-by-event v(2) 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.