The ac (alternating current) conductivity of Pb5Al3F19 between 293 and 743 K has been analyzed within a combined complex impedance, modulus, and permittivity formalism. The antiferroelectric phase IV to ferroelastic phase LII, and the phase m to paraelastic phase II, transitions have been characterized; the latter is shown to be accompanied by higher F- ion mobility above T=368 +/-5 K. A new dielectric anomaly observed isochronously in epsilon'(f,T) at 670 K corresponds to an expected, but hitherto unobserved, transition from phase II to the paraelectric prototype phase I of Pb5Al3F19 A F-19 NMR investigation between 125 and 430 K of F- ion diffusion properties in Pb5Al3F19 shows that half the anions have become mobile at the ferroelectric phase V to phase IV transition temperature and chat almost all the anions are mobile at the phase TV to phase III transition temperature. These motions are shown to be short range, and no correlation is found between phase Formation and F- ion diffusion properties in Pb5Al3F19 in the temperature range below 320 K.