Raman scattering, calorimetric and dielectric spectroscopy data for Cs5H3(SO4)(4) . H2O single crystals taken at 20-300 K are reported. The glass transition temperature, T-g, as determined from DSC, shows a remarkable hysteresis : 261 K on heating and 248 K on cooling. The change in the molar heat capacity is 27 J/mol . K. The dielectric data (30 kHz-2.2 MHz) show a pronounced dispersion whose relaxation frequency obeys an Arrhenius law. An increase in the isotropic component of Rayleigh light scattering was observed below T-g. Raman scattering data indicate a conservation of hexagonal crystal symmetry in the glassy phase, and a lowering of the site symmetry. The transition from dynamic to static disorder is discussed.