Vibrational energy relaxation is of critical importance for the light-controlled reactivity of transition-metal complexes. In time-resolved optical spectroscopies, it gives rise to pronounced spectral redistributions with complex band shifts and thus to nonexponential kinetics, all of which are very difficult to quantify. Here we study the vibrational relaxation dynamics of a pentacoordinated azido-cobalt(II) complex in liquid solution following its ultrafast charge-transfer excitation in the near-ultraviolet (UV). The complex is photochemically remarkably stable and returns within the experimental time resolution back to its quartet electronic ground state via internal conversion. The nonadiabatic transition effectively instantaneously converts the entire photon energy into kinetic energy of the vibrational degrees of freedom. The ensuing relaxation dynamics of the vibrationally highly excited complex are monitored as a function of time using femtosecond mid-infrared (MIR) spectroscopy in the antisymmetric stretching region of the azido ligand and occur on a time scale of a few tens of picoseconds. The dynamic evolution of the MIR spectrum due to vibrational cooling of the complex can be understood quantitatively within the framework of an anharmonic coupling model, which relies on an ab initio intramolecular cubic/quartic force field from density functional theory combined with second-order vibrational perturbation theory. The simulations suggest that the primary internal conversion preferentially dumps the excess energy into the low-frequency bending modes of the azido ligand, whereas its high-frequency stretching modes are barely affected by the initial nonadiabatic transition. Surprisingly, the two bending vibrations appear to relax independently of one another, each with its own characteristic cooling time.