Detailed magnetization measurements in La_5/8-yPr_yCa_3/8MnO₃, including magnetic relaxation properties, demonstrate the dynamic nature of the phase separated state in manganites. The difference between the field-cooled-cooling and zero-field-cooled magnetization curves signals the existence in the latter of blocked metastable states separated by high energy barriers. Results of the magnetic viscosity show that the system becomes unblocked in a certain temperature window, where large relaxation rates are observed. We propose a simple phenomenological model in which the system evolves through a hierarchy of energy barriers, which separates the coexisting phases. The calculated magnetization curves using this model reproduce all the qualitative features of the experimental data. The overall results allowed us to construct an H-T phase diagram, where frozen and dynamic phase separation regions are clearly distinguished.