Femtosecond light sources in the 3-5 μm region are highly sought after for numerous applications. While they can be generated by using nonlinear effects in optical fibers, the efficiencies and effectiveness of frequency conversion can be significantly enhanced by using ultrashort driving pulses. Here, we report on a few-cycle Cr:ZnS oscillator driving low-order soliton dynamics in soft-glass fibers. By selecting appropriate parameters, sub-two-cycle pulses or broad supercontinua spanning over 1.7 octaves from 1.6 to 5.1 μm can be generated at average power levels exceeding 300 mW. In the same setting, Raman-induced soliton self-frequency shifting has been exploited to generate sub-100-fs pulses continuously tunable from 2.3 to 3.85 μm with a conversion efficiency of ∼50%. These results demonstrate the vast potential of using Cr:ZnS or Cr:ZnSe lasers for powerful mid-infrared generation.