The full dimensional (15 degrees-of-freedom) quantum calculations of vibrational energies of H5O2+ are reported using the global potential energy surface (OSS) of Ojamäe et al. (J. Chem. Phys. 1998, 109, 5547). One set of calculations uses the diffusion Monte Carlo (DMC) method with a highly flexible initial trial wave function. This method is limited to the ground vibrational state, but produces what we believe is a highly accurate, benchmark energy and wave function for that state. The DMC wave function is analyzed to identify coordinates that are strongly correlated in zero-point fluctuations. A simple harmonic model is developed to elucidate the energetic consequences of these correlations. The other set of calculations is based on the code MULTIMODE, which does configuration interaction (CI) calculations using a basis determined from a vibrational self-consistent field (VSCF) Hamiltonian, but which uses a representation of the potential with mode coupling limited to a maximum of four modes. Good agreement is obtained between the DMC and the CI MULTIMODE energies for the ground vibrational state. When less sophisticated theoretical treatments are applied, either variational Monte Carlo or vibrational self-consistent field, fairly large errors are found. Vibrationally excited-state energies obtained with MULTIMODE are also reported.