Single-photon avalanche diodes (SPADs) that are sensitive to photons in the Short-wave infrared and extended short-wave infrared (SWIR and eSWIR) spectra are important components for communication, ranging, and low-light level imaging. The high gain, low excess noise factor, and widely tunable bandgap of AlxIn1-xAsySb1-y avalanche photodiodes (APDs) make them a suitable candidate for these applications. In this work, we report single-photon-counting results for a separate absorption, charge, and multiplication (SACM) Geiger-mode SPAD within a gated-quenching circuit. The single-photon avalanche probabilities surpass 80% at 80 K, corresponding with single-photon detection efficiencies of 33% and 12% at 1.55 µm and 2 µm, respectively.