By combining two independent approaches, inelastic neutron-scattering measurements and density-functionaltheory calculations, we study the spin waves in the collinear antiferromagnetic phase (AFM2) of Mn5Si3. We obtain its magnetic ground-state properties and electronic structure. This study allowed us to determine the dominant magnetic exchange interactions and magnetocrystalline anisotropy in the AFM2 phase of Mn5Si3. Moreover, the evolution of the spin excitation spectrum is investigated under the influence of an external magnetic field perpendicular to the anisotropy easy axis. The low-energy magnon modes show a different magnetic field dependence, which is a direct consequence of their different precessional nature. Finally, possible effects related to the Dzyaloshinskii-Moriya interaction are also considered.