The results of diffusion Monte Carlo (DMC) calculations of the ground and selected excited states of H-5(+) and its deuterated analogues are presented. Comparisons are made between the results obtained from two recently reported potential surfaces. Both of these surfaces are based on CCSD(T) electronic energies, but the fits display substantial differences in the energies of low-lying stationary points. Little sensitivity to these features is found in the DMC results, which yield zero-point energies based on the two surfaces that differ by between 20 and 30 cm(-1) for all twelve isotopologues of H-5(+). Likewise, projections of the ground state probability amplitudes, evaluated for the two surfaces, are virtually identical. By using the ground state probability amplitudes, vibrationally averaged rotational constants and dipole moments were calculated. On the basis of these calculations, all isotopologues are shown to be near-prolate symmetric tops. Further, in cases where the ion had a nonzero dipole moment, the magnitude of the vibrationally averaged dipole moment was found to range from 0.33 to 1.15 D, which is comparable to the dipole moments of H2D+ and HD2+. Excited states with up to three quanta in the shared proton stretch and one quantum in the in-phase stretch of the outer H-2 groups were also investigated. Trends in the energies and the properties of these states are discussed.