The stationary states of the kinetic mixed spin-2 and spin-5/2 Ising ferrimagnetic system with repulsive biquadratic coupling are examined within a mean-field approach under the presence of a time varying (sinusoidal) magnetic field. We employ Glauber-type stochastic dynamics to construct a set of coupled mean-field dynamic equations, and we solve these equations to find the phases in the system. We also investigate the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the dynamic phase transitions (DPTs) and obtain the DPT points. The phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane, and a comparison is made with the results of other kinetic mixed spin systems. We also study the behavior of the dynamic magnetic hysteresis and investigate the effects of the frequency on hysteresis properties, and we find the results are in good agreement with some previous theoretical and experimental works.