We present the design, fabrication and characterization of efficient fiber-to-chip grating couplers on a Germanium-on-Silicon (Ge-on-Si) and Germanium-on-silicon-on-insulator (Ge-on-SOI) platform in the 5 µm wavelength range. The best grating couplers on Ge-on-Si and Ge-on-SOI have simulated coupling efficiencies of -4 dB (40%) with a 3 dB bandwidth of 180 nm and -1.5 dB (70%) with a 3 dB bandwidth of 200 nm, respectively. Experimentally, we show a maximum efficiency of -5 dB (32%) and a 3 dB bandwidth of 100 nm for Ge-on-Si grating couplers, and a -4 dB (40%) efficiency with a 3 dB bandwidth of 180 nm for Ge-on-SOI couplers.