We present a new technique for empirically calibrating how the X-ray luminosity function (XLF) of X-ray binary (XRB) populations evolves following a star-formation event. We first utilize detailed stellar population synthesis modeling of far-UV to far-IR photometry of the nearby face-on spiral galaxy M51 to construct maps of the star-formation histories (SFHs) on subgalactic (~400 pc) scales. Next, we use the ~850 ks cumulative Chandra exposure of M51 to identify and isolate 2-7 keV detected point sources within the galaxy, and we use our SFH maps to recover the local properties of the stellar populations in which each X-ray source is located. We then divide the galaxy into various subregions based on their SFH properties (e.g., star-formation rate [SFR] per stellar mass [M*] and mass-weighted stellar age) and group the X-ray point sources according to the characteristics of the regions in which they are found. Finally, we construct and fit a parameterized XLF model that quantifies how the XLF shape and normalization evolves as a function of the XRB population age. Our best-fit model indicates the XRB XLF per unit stellar mass declines in normalization, by ~3-3.5 dex, and steepens in slope from ~10 Myr to ~10 Gyr. We find that our technique recovers results from past studies of how XRB XLFs and XRB luminosity scaling relations vary with age and provides a self-consistent picture for how the XRB XLF evolves with age.
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