Thermal and transport properties, as well as spectral characteristics of Rb5H7(PO4)4, have been investigated by several methods. It was shown that Rb5H7(PO4)4 undergoes a reversible phase transition at Tp ~ 237 °С. However, the interval of the high-temperature phase stability is quite narrow, about 15 °С. The initial dehydration event in Rb5H7(PO4)4 occurs at 200 °С. The conductivity measurements were performed under highly humidified conditions (PH2O ≈ 0.56 atm.) to suppress dehydration of the title salt. The phase transition leads to the sharp increase of proton conductivity up to 10−2 S/cm. The reverse transition goes slowly with significant hysteresis on cooling. Thus, the superprotonic conductivity of Rb5H7(PO4)4 was determined. The possibility of superionic phase stabilization by humidification was shown. The IR- and Raman spectra have been recorded at room temperature and discussed in relation to the crystal structure.