  Anisotropic flow coefficients, $v_n$, non-linear flow mode coefficients,
$\chi_{n,mk}$, and correlations among different symmetry planes, $\rho_{n,mk}$
are measured in Pb-Pb collisions at $\sqrt{s_\rm{NN}}=5.02$ TeV. Results
obtained with multi-particle correlations are reported for the transverse
momentum interval $0.2<p_\rm{T}<5.0$ GeV/$c$ within the pseudorapidity interval
$0.4<|\eta|<0.8$ as a function of collision centrality. The $v_n$ coefficients
and $\chi_{n,mk}$ and $\rho_{n,mk}$ are presented up to the ninth and seventh
harmonic order, respectively. Calculations suggest that the correlations
measured in different symmetry planes and the non-linear flow mode coefficients
are dependent on the shear and bulk viscosity to entropy ratios of the medium
created in heavy-ion collisions. The comparison between these measurements and
those at lower energies and calculations from hydrodynamic models places strong
constraints on the initial conditions and transport properties of the system.
