We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic mixed spin-1/2 and spin-5/2 Ising model under the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the set of mean-field dynamic equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The DPT points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain four fundamental phases and three coexistence or mixed phases, which strongly depend on interaction parameters. The phase diagrams are discussed and a comparison is made with the results of the other mixed spin Ising systems.