The room temperature structure of Ba(5)Al(3)F(19) has been solved using electron microscopy and synchrotron powder diffraction data. One-dimensional (1D) (27)Al and ultrafast magic-angle-spinning (MAS) (19)F NMR spectra have been recorded and are in agreement with the proposed structural model for Ba(5)Al(3)F(19). The (19)F isotropic chemical shift and (27)Al quadrupolar parameters have been calculated using the CASTEP code from the experimental and density functional theory geometry-optimized structures. After optimization, the calculated NMR parameters of both the (19)F and (27)Al nuclei show improved consistency with the experimental values, demonstrating that the geometry optimization step is necessary to obtain more accurate and reliable structural data. This also enables a complete and unambiguous assignment of the (19)F MAS NMR spectrum of Ba(5)Al(3)F(19). Variable-temperature 1D MAS (19)F NMR experiments have been carried out, showing the occurrence of fluorine ion mobility. Complementary insights were obtained from both two-dimensional (2D) exchange and 2D double-quantum dipolar recoupling NMR experiments, and a detailed analysis of the anionic motion in Ba(5)Al(3)F(19) is proposed, including the distinction between reorientational processes and chemical exchange involving bond breaking and re-formation.