The design of a fully explicit second-order scheme applied to the framework of non-conservative time dependent 1D hyperbolic problems, in the context of compressible multiphase flows with strong interacting discontinuities, is presented. The aim is to investigate an explicit second-order approximation for a non-conservative system, given by the five equation model of Kapila et al. (Physics of Fluids 2001). The discretization is based on a predictor-corrector scheme, which follows the concept of residual distributions in Ricchiuto and Abgrall (J. Comp. Physics 2010). The novelty of this work is the capability of the presented approximation to provide mesh convergence and to be easily extended to 2D and unstructured meshes. A benchmark on the two-phase compressible system for a stiffened gas verifies the robustness and convergence to the expected solution of the presented approximation.