The definition of particle rest mass in a 5D space, like the definition of mass in 4D general relativity, is difficult. We review 6 alternatives. It is plausible that the mass of a particle derives from the geometry of a 4D space embedded in a 5D space, and that the Klein-Gordon equation of 4D quantum theory is a wave equation in a conformal factor of 5D Kaluza-Klein theory. ©1999 American Institute of Physics.