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High-resolution cross-correlation spectroscopy (HRCCS) combined with adaptive optics has been enormously successful in advancing our knowledge of exoplanet atmospheres, from chemistry to rotation and atmospheric dynamics. This powerful technique now drives major science cases for ELT instrumentation including METIS/ELT, GMTNIRS/GMT, and MICHI/TMT, targeting biosignatures on rocky planets at 3-5 μm, but remains untested beyond 3.5 μm where the sky thermal background begins to provide the dominant contribution to the noise. We present 3.51-5.21 μm M-band CRIRES+/VLT observations of the archetypal young directly imaged gas giant β Pictoris b, detecting CO absorption at S/N = 6.6 at 4.73 μm and H2O at S/N = 5.7, and thus extending the use of HRCCS into the thermal background noise dominated infrared. Using this novel spectral range to search for more diverse chemistry, we report marginal evidence of SiO at S/N = 4.3, potentially indicative that previously proposed magnesium-silicate clouds in the atmosphere are either patchy, transparent at M-band wavelengths, or possibly absent on the planetary hemisphere observed. The molecular detections are rotationally broadened by the spin of β Pic b, and we infer a planetary rotation velocity of vsin(i) = 22 ± 2 km s-1 from the cross-correlation with the H2O model template, consistent with previous K-band studies. We discuss the observational challenges posed by the thermal background and telluric contamination in the M-band, the custom analysis procedures required to mitigate these issues, and the opportunities to exploit this new infrared window for HRCCS using existing and next-generation instrumentation.