In ferromagnets, the anomalous Hall effect (AHE) can exhibit time-dependent relaxation, including magnetic aftereffect and Barkhausen jumps, and thus provide insights into magnetic susceptibility and domain dynamics. Recently, a finite AHE has also been reported in compensated collinear magnets—termed altermagnets—which, due to their spin and crystal symmetries, combine properties usually attributed to either ferromagnets or antiferromagnets. To date, a possible time-dependent relaxation of the AHE in altermagnets has not been explored. Here, we study the Hall effect response of micrometer-scale Hall bars patterned into thin films of Mn₅Si₃, an altermagnet featuring a finite spontaneous AHE. Recording transport data as a function of time, at a fixed magnetic field magnitude, we observe a relaxation of the Hall voltage qualitatively and quantitatively similar to the magnetic aftereffect in ferromagnetic films. In addition, the Hall voltage time traces feature clear unidirectional jumps, which we interpret as Barkhausen jumps, i.e., as experimental evidence for abrupt reorientations of Hall vector domains in Mn₅Si₃. A quantitative analysis yields a Barkhausen length of around 18 nm in the Hall bar devices with the smallest width of 100 nm.