  We report on the first measurement of the triangular $v_3$, quadrangular
$v_4$, and pentagonal $v_5$ charged particle flow in Pb-Pb collisions at 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 $v_2$ and $v_3$
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.
