This contribution is an update of a previous presentation of 5D matter- wave optics and interferometry with a correction of some algebraic errors. Electromagnetic interactions are explicitly added in the 5D metric tensor in complete analogy with Kaluza's work. The 5D Lagrangian is rederived and an expression for the Hamiltonian suitable for the parabolic approximation is presented. The corresponding equations of motion are also given. The 5D action is shown to cancel for the actual trajectory which is a null geodesics of the 5D metric. This presentation is mainly devoted to the classical aspects of the theory and only general consequences for the quantum phase of matter-waves are outlined. The application to Bord\'e- Ramsey interferometers is given as an illustration.