Diverse slip behaviors are observed in HfNbTaTiZr refractory high-entropy alloy during tensile tests. Slow-avalanche and fast-runaway phases are identified by analyzing scaling relationships among slip statistics. Slow avalanches display a scaling collapse in temporal shapes, aligning with mean-field slip theory, while system-spanning fast-runaway avalanches show a Gaussian shape, indicating rapid nucleation due to dynamic weakening. Through time scale analysis, we construct a nonequilibrium phase diagram elucidating the influence of temperature and strain rate variations on solute-dislocation interaction.