Inelastic neutron scattering measurements are performed on single crystals of the antiferromagnetic compound Mn_{5}Si_{3} in order to investigate the relation between the spin dynamics and the magnetothermodynamics properties. It is shown that, among the two stable antiferromagnetic phases of this compound, the high temperature one has an unusual magnetic excitation spectrum where propagative spin waves and diffuse spin fluctuations coexist. Moreover, it is evidenced that the inverse magnetocaloric effect of Mn_{5}Si_{3}, the cooling by adiabatic magnetization, is associated with field induced spin fluctuations.