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The study of geometrically frustrated systems with antiferromagnetically ordered spins on a two-dimensional lattice has recently gained considerable attention for their exotic quantum magnetic properties. In order to explore effects related to quantum magnetism we investigate the magnetization dynamics of Na₂BaMn(PO₄)₂, a compound with S=5/2. By coaligning hundreds of single crystals with a robot and employing inelastic neutron scattering measurements performed on a cold triple axis spectrometer we determine the magnetic propagation vector and the low energy spin excitations of Na₂BaMn(PO₄)₂ at mK temperatures. We obtain results in its spin polarized state and extract the relevant exchange interactions. Furthermore, we compare our results with the Co (with S=1/2) and Ni (with S=1) counterparts and we find similarities not only in the temperature- magnetic field (H-T) phase diagrams, but also in the spin excitation spectra.