The highly flexible CH5+ molecular ion has been shown by ab initio calculations to have 120 symmetrically equivalent minima of C-s symmetry in its ground electronic state. Each minimum has the structure of a hydrogen molecule bound to the apex of a CH3+ pyramid, with the hydrogen molecule approximately perpendicular to the C-3 axis. Complete proton rearrangement, making all minima accessible to each other, is possible as a result of two large-amplitude internal motions: an internal rotation about the C-3 axis with an ab initio barrier of 30 cm(-1) and an internal flip motion with an ab initio barrier of 300 cm(-1) that exchanges protons between the H-2 and CH3+ groups. We calculate the structure of the J = 2 <-- 1, and 1 <-- 0 rotational transitions for CH5+ and CD5+. The calculation proceeds in two stages. The first stage involves calculating rotation-torsion energies, and the second stage involves a matrix diagonalization to include the flip tunneling. In the first stage the rotation-torsion energies are calculated using the exact rotation-torsion Hamiltonian with a fully relaxed ab initio minimum energy path for internal rotation. The rotation-torsion energy levels and the final proton rearrangement energies that we obtain here are significantly different from those obtained earlier by us using the approximate precessing-internal-rotor Hamiltonian of X.-Q. Tan and D. W. Pratt [J. Chem. Phys. 1994, 100, 7061] that they developed for application to p-toluidine. This is partly because the angle of tilt between the precessing C-3 axis of the CH3+ internal rotor and the C-2 axis of the CH2 frame is too large for the approximate precessing-internal-rotor Hamiltonian to be appropriate and partly because the CH3+ group significantly distorts as it internally rotates. In the final calculation we include the contribution to the torsional barrier from the zero point energies of the other (high-frequency) vibrations, the effect of centrifugal distortion, and the effect of second-order rotation-vibration interactions (i.e, the alpha constants).