We report on a first of its kind, to our knowledge broadband amplification in a Fe:CdSe single crystal in the mid-IR beyond 5 µm. The experimentally measured gain properties demonstrate saturation fluence close to 13 mJ/cm2 and support the bandwidth up to 320 nm (full width at half maximum). Such properties allow the energy of the seeding mid-IR laser pulse, generated by an optical parametric amplifier, to be pushed up to more than 1 mJ. Dispersion management with bulk stretcher and prism compressor enables 5-µm laser pulses of 134-fs duration, providing access to multigigawatt peak power. Ultrafast laser amplifiers based on a family of Fe-doped chalcogenides open the route for wavelength tuning together with energy scaling of mid-IR laser pulses that are strongly demanded for the areas of spectroscopy, laser-matter interaction, and attoscience.