Recent advancements in near-infrared (NIR) spectroscopy have opened new opportunities for studying multiple stellar populations in globular clusters (GCs), particularly for newly discovered clusters in the inner Milky Way. While optical spectroscopy has traditionally played a primary role in detailed chemical abundance studies of GCs, the increasing discovery of GCs in highly reddened environments underscores the need for robust NIR spectroscopic methods. To evaluate the utility of high-resolution NIR spectroscopy for studying multiple stellar populations, we observed six stars in M5, a well-studied halo GC, using the recently commissioned IGRINS-2 spectrograph on the Gemini-North telescope. Our chemical abundance measurements in the NIR wavelength range show good agreement with those derived from high-resolution optical spectroscopy, with minor systematic offsets in elements such as Na and Mg. In addition, the measured chemical abundance ratios clearly reproduce the distinctive patterns of multiple stellar populations, including the Na-O anti-correlation. The ability of NIR spectroscopy to measure C, N, and O abundances with high precision further enhances its utility for studying chemical properties of stars and GCs. Our findings demonstrate that IGRINS-2 and similar instruments have significant potential to advance our understanding of GC formation, stellar chemical evolution, and the evolutionary history of the Milky Way.