We have performed Time Dependent Density Functional Theory (TDDFT) calculations employing a cluster model of the core excitation spectra of vanadium pentoxide, V(2)O(5). The excitation energies and dipole transition moments are determined for all the core edges, vanadium and oxygen K- and vanadium L-edges, treating them at the same level of accuracy. The agreement between the TDDFT theoretical spectra and the experimental data is rather good, particularly at the V and O K-edges. A quantitative reproduction of the fine pre-edge structures appears more difficult for the V L-edge. The comparison between the TDDFT results and the results obtained at the simpler one electron Kohn-Sham (KS) level indicates that the V and O K edges can be correctly described within a single particle approximation (KS), while the strong modification of the V L-edge structures from the KS to the TDDFT description emphasizes the importance of configuration mixing to treat the metal 2p excitations. The origin of the calculated pre-edge features is analyzed in detail with the help of the atom-projected density-of-states of the unoccupied levels. This analysis emphasizes the V 3d dominant character of the final states in the conduction band, probed by the V L-absorption. The strong octahedral distortion of the V(2)O(5) structure allows the mixing of the 3d state with the V 4p components, which are mapped by the oscillator strength in the V K-edge spectrum. The high intensity of the O 1s transitions reflects the presence of a significant O 2p component in the conduction band.