Comprehensive studies of the temperature-dependent properties of amorphous Fe-Co-Si-B-Mn alloys have been conducted using differential scanning calorimetry and induction vibromagnetometry. It is established that the investigated alloys exhibit a two-stage crystallization process; the presence of cobalt in the composition leads to a non-monotonic character of the thermomagnetic curves. The phase transition temperatures, including the Curie temperature, were determined. The spin-wave stiffness constant was calculated using a modified Bloch's law. The research results are important for understanding the effect of cobalt doping on the magnetic properties of iron-based amorphous alloys.