Utilizing the path probability method, we investigated nonequilibrium magnetic features in a mixed spin (2, 5/2) Ising model Hamiltonian composed of bilinear and crystal-field interactions in the presence of an external oscillating magnetic field. We numerically solved the time dependence of average magnetizations to find the phases in the system. We examined the dynamic magnetizations to obtain dynamic phase transition (DPT) temperatures, the nature of the DPTs, and phases in the system. The dynamic phase diagrams (DPDs) were constructed in reduced temperature and the amplitude of oscillating magnetic field plane for various interaction parameters. We observed that the system gives very rich and interesting topological behaviors of DPDs, such as up to two dynamic tricritical points, six critical end points, a double critical end points, a zero-temperature critical point, one inverse critical end point and a quadruple point depending on interaction parameters. The system also exhibits paramagnetic, six distinct ferrimagnetic and three different nonmagnetic phases as well as up to eleven different mixed or hybrid phases. In addition, the system exhibits the reentrant behavior.