The authors propose an easy and effective variant of the realization of the dynamical symmetry of hydrogen-like atoms in five-dimensional space, based on the relationship between the Schrodinger equation for the isotropic harmonic oscillator in four-dimensional complex space and the Schrodinger equation for the one-electron atom in five-dimensional space. By the use of the path integral they also establish the relationship between the Coulomb Green function and the Green function for the isotropic harmonic oscillator in four-dimensional complex space.