This paper presents an Euleriean model for the simulation of compressible two-phase flow problems. The starting point of the study is a seven equation, two pressure, two velocity model. This model contains relaxation terms that drive the systems toward pressure and velocity equilibrium. We perform an asymptotic analysis of this system in the limit of zero relaxation time and derive a five equation hyperbolic reduced system. We study the mathematical properties of the system, the structure of the waves and the expression of the Riemann's invariants. We then describe two different numerical approximation schemes for this system. The first one relies on a linearized Riemann solver while the second uses more heavily the mathematical structure of the system and relies on a linearization of the characteristic relations. Finally, we present some numerical experiments and comparison with the results obtained by the two pressure, two velocity model as well as some test cases in interface computations.