Ultrafast mid-infrared (IR) coherent radiation plays an important role in strong-field physics, wherein the use of longer wavelengths has reduced the optical intensities needed to drive light-matter interactions by orders of magnitude in comparison to near-IR radiation. Optimizing parametric interactions for generation and characterization of mid-IR pulses is an enabling step for those applications. We report on the production of >50 µJ femtosecond pulses centered at 5 µm in a two-stage optical parametric amplifier (OPA) based on ZnGeP2, a high-performance optical material in this spectral region. The OPA is pumped by an ultrafast 2-µm source. Amplified pulses have been characterized by parametric upconversion, enabling the use of standard silicon detectors. A numerical model of the system has been developed and tested to control dispersion, group-velocity mismatch, and off-axis parametric fluorescence. The source architecture is suitable for production of mJ-level mid-IR ultrafast pulses without the use of chirped-pulse amplification, where convenient pumping could be realized directly by mid-IR laser sources based on materials such as Cr:ZnSe or Cr:ZnS.