The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for π ±, K± and p+p in Pb-Pb collisions at √sNN = 2.76 TeV were measured with the ALICE detector at the Large Hadron Collider. The results were obtained with the Scalar Product method, correlating the identified hadrons with reference particles from a different pseudorapidity region. Effects not related to the common event symmetry planes (non-flow) were estimated using correlations in pp collisions and were subtracted from the measurement. The obtained flow coefficients exhibit a clear mass ordering for transverse momentum (pT) values below ≈ 3 GeV/c. In the intermediate pT region (3 <pT <6 GeV/c), particles group at an approximate level according to the number of constituent quarks, suggesting that coalescence might be the relevant particle production mechanism in this region. The results for pT <3 GeV/c are described fairly well by a hydrodynamical model (iEBE-VISHNU) that uses initial conditions generated by A Multi-Pha