Extensive X-band and Q-band FMR experiments have been performed in the Mn5Ge3 epitaxial films with thicknesses varying between 4.5 and 68 nm. FMR signals were recorded in the temperature range between 15 and 295 K, at different orientations of magnetic field with respect to the film plane. In addition to the acoustic FMR mode with well defined resonance field, originating from inside the magnetic domains, a broad absorption line has been observed at low fields and attributed to the unresolved spectrum of FMR modes having the origin in flux closure caps. The FMR results have been discussed in the context of the domain structure computed with the use of OOMMF micromagnetic calculations and giving good agreement with the experimental hysteresis curves. From the Q-band experiments, where the FMR signal is observed in the magnetically saturated sample, the uniaxial anisotropy constant in films with different thicknesses has been determined as a function of temperature. This FMR study provides the evidence that the strong uniaxial anisotropy observed in epitaxial thin films of Mn5Ge3 leads to the formation of a stripe domain structure above 25 nm, in agreement with the published reports on magnetization studies in these films. It also eliminates a possible confusion that may arise from previously published FMR studies on films grown with the same method, which led their authors to conclude that the shape anisotropy can force the magnetization to the in-plane orientation in this thickness range and even above it.