  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.
