Measurements of the azimuthal anisotropy in lead-lead collisions at s NN = 5.02 TeV are presented using a data sample corresponding to 0.49 nb - 1 integrated luminosity collected by the ATLAS experiment at the LHC in 2015. The recorded minimum-bias sample is enhanced by triggers for "ultra-central" collisions, providing an opportunity to perform detailed study of flow harmonics in the regime where the initial state is dominated by fluctuations. The anisotropy of the charged-particle azimuthal angle distributions is characterized by the Fourier coefficients, v 2 - v 7 , which are measured using the two-particle correlation, scalar-product and event-plane methods. The goal of the paper is to provide measurements of the differential as well as integrated flow harmonics v n over wide ranges of the transverse momentum, 0.5 < p T < 60 GeV, the pseudorapidity, | η | < 2.5, and the collision centrality 0-80%. Results from different methods are compared and discussed in the context of previous and recent measurements in Pb+Pb collisions at s NN = 2.76 TeV and 5.02 TeV . In particular, the shape of the p T dependence of elliptic or triangular flow harmonics is observed to be very similar at different centralities after scaling the v n and p T values by constant factors over the centrality interval 0-60% and the p T range 0.5 < p T < 5 GeV.