Due to the long spin lifetime and its optical and electrical properties, GeSn is a promising candidate for the integration of spintronics, photonics, and electronics. Here, we investigate the photoinduced inverse spin-Hall effect in a GeSn alloy with 5% Sn concentration. We generate a spin-polarized electron population at the Gamma point of the GeSn conduction band by means of optical orientation, and we detect the inverse spin-Hall effect signal coming from the spin-to-charge conversion in GeSn. We study the dependence of the inverse spin-Hall signal on the kinetic energy of the spin-polarized carriers by varying the energy of the impinging photons in the 0.5-1.5eV range. We rationalize the experimental data within a diffusion model which explicitly accounts for momentum, energy, and spin relaxation of the spin-polarized hot electrons. At high photon energies, when the spin relaxation is mainly driven by phonon scattering, we extract a spin-Hall angle in GeSn which is more than ten times larger than the one of pure Ge. Moreover, the spin-charge interconversion for electrons lying at the Delta valleys of GeSn results to be approximate to 4.3 times larger than the one for electrons at L valleys.