A photodissociation spectrum of H-5+ between 5400 and 10000 cm-1 has been measured by monitoring the H-3+ photofragment yield. Four new bands have been observed at 6690, 7130, 7490, and 7770 cm-1, and they are interpreted to be vibrational predissociation bands resulted from exciting 2-nu-2, nu-1 + nu-2, 2-nu-1 and 2-nu-1 + nu-8 modes of H-5+. The observed bands are broad; their rotational structures were not resolved by the 1 cm-1 linewidth of the laser. Combining the results of this work with those of Okumura et al., we have obtained harmonic frequencies and anharmonicity constants of the nu-1 and nu-2 bands: omega-1 = 4400 cm-1, (omega-2 = 4060 cm-1, chi-11 = -170 cm-1, chi-22 = -190 cm-1, and chi-12 = -310 cm-1. Comparison of these results with the available theoretical results is given.