We present a spectral investigation of X-ray binaries 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, and present the spectral parameters of sources with L >2x10^37 erg/s. 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 Msol. 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 Msol 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 >= 5x10^38 erg/s for the XB population of early-type galaxies; for older stellar populations, there are fewer stars >1 Msol, which are required to form the more luminous sources.
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