In this paper, we explicitly construct an asymptotic W-5 symmetry algebra of the three-dimensional anti-de Sitter (AdS(3)) higher spin gravity. We use an sl(5, R) circle plus sl (5, R) Lie algebra valued Chern-Simons gauge theory with a negative cosmological constant, and its asymptotic symmetry algebra is explicitly calculated as two copies of the classical W-5 algebra with central charge c. Our results can be interpreted as a spin 5 extension of AdS(3) gravity and a proof of how the higher spin Ward identities and the asymptotic W-5 symmetry algebra is derived from the higher spin bulk field equations of motion. This higher spin asymptotic W-5 symmetry algebra contains a finite number of conformal primary spin s: s = 2, 3, 4, 5. We also indicated how to introduce chemical potentials and holonomy conditions associated with these higher spin charges in AdS(3) higher spin gravity in a manner that it preserves the asymptotic symmetry algebra. Published by AIP Publishing.