The investigations of the interconnection between micro- and macroscopic properties of materials hosting noncollinear antiferromagnetic ground states are challenging. These forefront studies are crucial for unraveling the underlying mechanisms at play, which may prove beneficial in designing cutting-edge multifunctional materials for future applications. In this context, Mn5Si3 has regained scientific interest since it displays an unusual and complex ground state, which is considered to be the origin of the anomalous transport and thermodynamic properties that it exhibits. Here, we report the magnetic exchange couplings of the noncollinear antiferromagnetic phase of Mn5Si3 using inelastic neutron scattering measurements and density functional theory calculations. We determine the ground-state spin configuration and compute its magnon dispersion relations which are in good agreement with the ones obtained experimentally. Furthermore, we investigate the evolution of the spin texture under the application of an external magnetic field to demonstrate theoretically the multiple field-induced phase transitions that Mn5Si3 undergoes. Finally, we model the stability of some of the material's magnetic moments under a magnetic field and we find that very susceptible magnetic moments in a frustrated arrangement can be tuned by the field.