A global nine-dimensional potential energy surface (GPES) for the adiabatic ground state of the H-5 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 H-5 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.