Measurements of the azimuthal anisotropy in lead–lead collisions at $\sqrt{s_{_\text {NN}}}$ = 5.02 TeV are presented using a data sample corresponding to 0.49 ${\mathrm {nb}}^{-1}$ 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 $<$ 60 GeV, the pseudorapidity, $|\eta |<$ 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 $\sqrt{s_{_\text {NN}}}$ = 2.76 $\mathrm{TeV}$ and 5.02 $\mathrm{TeV}$ . In particular, the shape of the $p_{\mathrm{T}}$ dependence of elliptic or triangular flow harmonics is observed to be very similar at different centralities after scaling the $v_{n}$ and $p_{\mathrm{T}}$ values by constant factors over the centrality interval 0–60% and the $p_{\mathrm{T}}$ range 0.5 $< p_{\mathrm{T}}<$ 5 GeV.