We report on the first measurement of the triangular v3, quadrangular v4, and pentagonal v5 charged particle flow in Pb-Pb collisions at sqrt(s(NN)) = 2.76 TeV measured with the ALICE detector at the CERN Large Hadron Collider. We show that the triangular flow can be described in terms of the initial spatial anisotropy and its fluctuations, which provides strong constraints on its origin. In the most central events, where the elliptic flow v2 and v3 have similar magnitude, a double peaked structure in the two-particle azimuthal correlations is observed, which is often interpreted as a Mach cone response to fast partons. We show that this structure can be naturally explained from the measured anisotropic flow Fourier coefficients.