The high-pressure forms of ice, phases III and V, are the equilibrium solids in contact with liquid water at pressures between 2.5 - 5.5 kbar. Consequently, their properties are important to calculating the volume changes caused by freezing of subsurface oceans inside icy planetary bodies and the buoyancy of icy volcanic melts. To quantify these properties we propose to measure the P-T dependence of the equation of state of ices III and V. Since both have small stability fields, we must quench these phases to < 100 K at high pressure. Furthermore, both phases are inhibited by the use of He pressure media. We propose a unique experiment in which argon is used to synthesize ices III and V, whereafter the system is purged with He so that we can cool < 100 K without freezing the pressure medium. This work will provide accurate equation of state parameters for planetary modelling.