Five-phase electric machines possess several distinct features and are sometimes considered in vehicular power systems and various special-purpose energy sources. Design and analysis of such machine-converter systems are highly dependent on simulation software programs, where accurate and numerically efficient dynamic models of five-phase synchronous machines are essential. Depending on levels of fidelity and interfacing compatibility, the traditional models for five-phase machines include the coupled-circuit-phase-domain (CCPD) and qd0 models. To achieve a computationally-efficient model suitable for many simulation programs, in this paper, a new constant-parameter voltage-behind-reactance (CPVBR) model is proposed for five-phase synchronous machines where a simple interfacing circuit is achieved with constant RL branches. The proposed model is validated by experimental measurements and simulation studies. The proposed CPVBR model is demonstrated to have superior numerical efficiency and simulation speed compared to the existing conventional models.