A global nine-dimensional potential energy surface (GPES) for the adiabatic ground state of the H5 system which fits the ab initio data, reported in the previous paper of this series, has been obtained (root-mean-square error 2.2 kcal/mol). The global fitting procedure is an extension of the corresponding procedure for triatomic and tetra-atomic systems including the functional form previously proposed by the authors. The H5 GPES obtained here is totally symmetric with respect to permutations of the hydrogen atoms and satisfies the criteria needed to be used in scattering calculations.