A five-dimensional field tensor with components determined by the derivatives with respect to space, time and to the fifth coordinate, of the electromagnetic four-potential and of a scalar non-electromagnetic potential follows from a five-dimensional extension of the Dirac equation. With this tensor as a basis, the Maxwell-Nordström equations are derived. It is shown that when the fifth coordinate is identified with an imaginary time-coordinate, the Maxwell-Nordström equations describe electromagnetic phenomena together with hypothetical gravitomagnetic phenomena. Plane electromagnetic waves and gravitomagnetic waves in the vacuum are discussed.