Measurements of the azimuthal anisotropy in lead-lead collisions at Formula omitted = 5.02 TeV are presented using a data sample corresponding to 0.49 Formula omitted 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, Formula omitted- Formula omitted, 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 Formula omitted over wide ranges of the transverse momentum, 0.5 Formula omitted 60 GeV, the pseudorapidity, Formula omitted 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 Formula omitted = 2.76 Formula omitted and 5.02 Formula omitted. In particular, the shape of the Formula omitteddependence of elliptic or triangular flow harmonics is observed to be very similar at different centralities after scaling the Formula omitted and Formula omittedvalues by constant factors over the centrality interval 0-60% and the Formula omittedrange 0.5 Formula omitted 5 GeV.