Understanding the spectroscopy and dynamics of H-5(+) is central in gaining insights into the H-3(+) + H-2 -> H-5(+) -> H-2 + H-3(+) proton transfer reaction. This molecular ion exhibits large-amplitude vibrations, which allow for the transfer of a proton between H-3(+) and H-2 even in its ground vibrational state. With vibrational excitation, the number of open channels for permutations of protons increase. In this work, the minimized energy path variant of diffusion Monte Carlo is used to investigate how the energetically accessible proton permutations evolve as H-5(+) is dissociated into H-3(+) + H-2. Two mechanisms for proton permutation are investigated. The first is the proton hop, which correlates to large-amplitude vibrations of the central proton in H-5(+). The second is the exchange of a pair of hydrogen atoms between H-3(+) and H-2. This mechanism requires several proton hops along with a 120 degrees rotation of H-3(+) within the H-5(+) molecular ion. This analysis shows that while there is a narrow region of configuration space over which both isomerization processes are energetically accessible, full permutation of the five protons in H-5(+) more likely occurs through a stepwise mechanism Such full permutation of the protons becomes accessible when the shared proton stretch is excited to the v(pt) = 2 or 3 excited state. The effects of deuteration and rotational excitation of the H-2 and H-3(+) products are also investigated. Deuteration inhibits permutation of protons, while rotational excitation has only a small impact on these processes.