The dynamic response of magnetically ordered materials to an ultrashort external stimulus depends on microscopic parameters, such as magnetic moment, exchange, and spin–orbit interactions. Whereas it is well established that, in multicomponent magnetic alloys and compounds, the speed of demagnetization and spin switching processes has an element-specific character, the magnetization damping was assumed to be a universal parameter for all constituent magnetic elements irrespective of their different spin–orbit couplings and electronic structure. Herein, experimental and theoretical evidence for an element-specific magnetic damping parameter is provided by investigating the ultrafast magnetization response of a high-anisotropy ferrimagnetic DyCo5 alloy to femtosecond laser excitation. Strikingly different demagnetization and remagnetization dynamics of Dy and Co magnetic moments is revealed by employing femtosecond laser pump–X-ray magnetic circular dichroism probe measurements combined with atomistic spin dynamics (ASD) simulations using ab initio calculated parameters. These observations, fully corroborated by the ASD simulations, are linked to the element-specific spin–orbit coupling strengths of Dy and Co, which are incorporated in the phenomenological magnetization damping parameters. These findings can be used as a recipe for tuning the speed and magnitude of laser-driven magnetic processes and consequently allow control over various dynamic functionalities in multicomponent magnetic materials.