We present the measurement and analysis of five new (D 2 O) 5 bands via vibration-rotation-tunneling (VRT) spectroscopy as well as a preliminary description of a second (H 2 O) 5 band. The vibrationally averaged rotational constants of all five fitted bands agree well with those from the two previously observed (D 2 O) 5 bands and confirm that the pentamer averages to a symmetric, quasi-planar structure on the time scale of our experiment. While the spectrum of the first two bands, located at 50.7 cm -1 (1.52 THz) and 27.3 cm -1 (0.82 THz) are indicative of unperturbed oblate rotors, the three remaining (D 2 O) 5 bands centered at 47.7 cm -1 (1.43 THz), 45.4 cm -1 (1.36 THz), and 45.0 cm -1 (1.35 THz) are severely perturbed by first-order Coriolis coupling. This represents the first observation of this perturbation in the perdeuterated water pentamer, as well as the first observation of transitions between degenerate states of the torsional-puckering manifold. Unlike transitions from the (H 2 O) 5 band observed by Brown et al. at 89.0 cm -1 and the 103.8 cm -1 band that we report here, none of the individual rovibrational transitions of any of the five (D 2 O) 5 bands demonstrate spectral splittings due to bifurcation tunneling. We conclude, through careful analysis of these water pentamer bands, that at least three torsional-puckering manifolds have been probed and that the lowest-energy manifold is highly compacted. A plausible water pentamer torsional-puckering correlation diagram is proposed, though additional experimental data are required to unambiguously establish the energies of the torsional-puckering levels.