We present a spectral investigation of X-ray binaries (XBs) in NGC 5128 (Cen A), using six 100 ks Chandra observations taken over two months in 2007. We divide our sample into thermally and non-thermally dominated states based on the behavior of the fitted absorption column N H, and present the spectral parameters of sources with Lx ≳ 2 × 10 37 erg s-1. The majority of sources are consistent with being neutron star low-mass X-ray binaries (NS LMXBs) and we identify three transient black hole (BH) LMXB candidates coincident with the dust lane, which is the remnant of a small late-type galaxy. Our results also provide tentative support for the apparent "gap" in the mass distribution of compact objects between ∼2-5 M ⊙. We propose that BH LMXBs are preferentially found in the dust lane, and suggest this is because of the younger stellar population. The majority (∼70%-80%) of potential Roche lobe filling donors in the Cen A halo are ≳ 12 Gyr old, while BH LMXBs require donors ≳ 1 M ⊙ to produce the observed peak luminosities. This requirement for more massive donors may also explain recent results that claim a steepening of the X-ray luminosity function with age at Lx ≥ 5 × 1038 erg s-1 for the XB population of early-type galaxies; for older stellar populations, there are fewer stars ≳ 1 M ⊙, which are required to form the more luminous sources.