The appearance of a "liquid-like" proton T-2 and the large value of the proton self-diffusion coefficient D = (2.8 - 4.4) X 10(-8) cm(2)/s above T-c=414 K demonstrate the existence of fast protonic conductivity in Cs5H3(SO4)(4) . H2O in this phase. Proton NMR linewidth transitions occur around 300 and 240 K demonstrating the slowing down of the motion of acid protons and the freeze-out of crystal water reorientations.