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In this paper, we consider the Riemann problem for a five-equation, two-pressure (5E2P) model proposed by Ransom and Hicks for an isentropic compressible gas-liquid two-phase flows. The model is given by a strictly hyperbolic, non-conservative system of five partial differential equations (PDEs). We investigate the structure of the Riemann problem and construct an approximate solution for it. We solve the Riemann problem for this model approximately assuming that all waves corresponding to the genuinely nonlinear characteristic fields are rarefaction and discuss their properties. To verify the solver, a series of test problems selected from the literature are presented. [ABSTRACT FROM AUTHOR]