This paper fulfils the programme announced in part IV of the series by examining the detailed application of the general quantum theory of fluids to liquid He II. It is shown that although the classical laws of hydrodynamics and thermodynamics are formally obeyed by the quantum liquid, important divergences arise in the manner of their interpretation. Without introducing any assumption other than the validity of the general laws of quantum mechanics, it is possible to explain qualitatively and quantitatively the well-known properties of liquid helium, including the thermodynamic discontinuity, the thermomechanical effect, the transfer effect, and the presence of thermal waves in the liquid. The connexion with earlier theories is traced, and it is shown that although they are in agreement with the theory here proposed in certain respects, their fundamental concepts are in need of considerable revision. The theory can be applied with slight changes to the phenomenon of superconductivity.