We study the nonequilibrium aspects of the kinetics of a mixed spin-1 and spin-5/2 Ising system, including the biquadratic nearest-neighbor pair interaction (K) and the crystal-field interaction (D), tinder the presence of a time-dependent oscillating external magnetic field within a mean-field approach. The set of mean-field dynamic equations is obtained by employing the Glauber transition rates. We investigate the time variations of the average order parameters to find the phases in the system. We also study the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the phase transitions and to obtain the dynamic phase transition (DPT) points. The dynamic phase diagrams are presented in three different planes. The phase diagrams are discussed, and a comparison is made with the results of other kinetic mixed spin Ising systems.