We examine a diffuse emission region near the center of SNR 0509-67.5 to determine its nature. Within this diffuse region we observe a point-like source that is bright in the near-IR, but is not visible in the B and V bands. We consider an emission line observed at 6766 angstrom and the possibilities that it is Ly alpha, H alpha, and [O II] lambda 3727. We examine the spectral energy distribution (SED) of the source, comprised of Hubble Space Telescope B, V, I, J, and H bands in addition to Spitzer/IRAC 3.6, 4.5, 5.8, and 8 mu m bands. The peak of the SED is consistent with a background galaxy at z approximate to 0.8 +/- 0.2 and a possible Balmer jump places the galaxy at z approximate to 0.9 +/- 0.3. These SED considerations support the emission line's identification as [O II] lambda 3727. We conclude that the diffuse source in SNR 0509-67.5 is a background galaxy at z approximate to 0.82. Furthermore, we identify the point-like source superposed near the center of the galaxy as its central bulge. Finally, we find no evidence for a surviving companion star, indicating a double-degenerate origin for SNR 0509-67.5.