The metallic compound Mn5Si3 hosts a series of antiferromagnetic phases that can be controlled by external stimuli, such as temperature and magnetic field. In this work, we investigate the spin-excitation spectrum of bulk Mn5Si3 by combining inelastic neutron scattering measurements and density functional theory calculations. We study the evolution of the dynamical response under external parameters and demonstrate that the spin dynamics of each phase is robust against any combination of temperature and magnetic field. In particular, the high-energy spin dynamics is very characteristic of the different phases consisting of either spin waves or broad fluctuation patterns. This data set contains the data relevant to performing the spin dynamics simulations with the Spirit code, the spin-wave calculations with the SWIS code, and the neutron scattering experimental data.