The rotational spectrum of dinitrogen pentoxide (N2O5) has been investigated between 8 to 25 GHz at a rotational temperature of similar to 2.5 K using a pulsed-molecular-beam Fourier-transform microwave spectrometer. Two weak b-dipole spectra are observed for two internal-rotor states of the molecule, with each spectrum poorly characterized by an asymmetric-rotor Hamiltonian, The observation of only b-type transitions is consistent with the earlier electron-diffraction results of McClelland et al. [J. Am, Chem. Sec. 105, 3789 (1983)] which give a C-2 symmetry molecule with the b inertial axis coincident with the C-2 axis. Analysis of the N-14 nuclear hyperfine structure demonstrates that the two nitrogen nuclei occupy either structurally equivalent positions or are interchanging inequivalent structural positions via tunneling or internal rotation at a rate larger than similar to 1 MHz. For the two internal rotor states, rotational levels with K-a + K-c even have I-N = 0, 2, while levels with K-a + K-c odd have I-N = 1, where I-N is the resultant nitrogen nuclear spin, This observation establishes that the equilibrium configuration of the molecule has a twofold axis of symmetry. Guided by ab initio and dynamical calculations which show a planar configuration is energetically unfavorable, we assign the spectrum to the symmetric and antisymmetric tunneling states of a C-2 symmetry N2O5 with internal rotation tunneling of the two NO2 groups via a geared rotation about their respective C-2 axes. Because of the Bose-Einstein statistics of the spin-zero oxygen nuclei, which require that the rotational-vibrational-tunneling wave functions be symmetric for interchange of the O nuclei, only four of the ten vibrational-rotational-tunneling states of the molecule have nonzero statistical weights. Model dynamical calculations suggest that the internal-rotation potential is significantly more isotropic than implied by the electron-diffraction analysis.