We present a catalog of 5039 broad absorption line (BAL) quasars (QSOs) in the Sloan Digital Sky Survey (SDSS) Data Release 5 (DR5) QSO catalog that have absorption troughs covering a continuous velocity range >= 2000 km/s. We have fit ultraviolet (UV) continua and line emission in each case, enabling us to report common diagnostics of BAL strengths and velocities in the range -25,000 to 0 km/s for SiIV $\lambda$1400, CIV $\lambda$1549, AlIII $\lambda$1857, and MgII $\lambda$2799. We calculate these diagnostics using the spectrum listed in the DR5 QSO catalog, and also for spectra from additional SDSS observing epochs when available. In cases where BAL QSOs have been observed with Chandra or XMM-Newton, we report the X-ray monochromatic luminosities of these sources. We confirm and extend previous findings that BAL QSOs are more strongly reddened in the rest-frame UV than non-BAL QSOs and that BAL QSOs are relatively X-ray weak compared to non-BAL QSOs. The observed BAL fraction is dependent on the spectral signal-to-noise (S/N); for higher-S/N sources, we find an observed BAL fraction of approximately 15%. BAL QSOs show a similar Baldwin effect as for non-BAL QSOs, in that their CIV emission equivalent widths decrease with increasing continuum luminosity. However, BAL QSOs have weaker CIV emission in general than do non-BAL QSOs. Sources with higher UV luminosities are more likely to have higher-velocity outflows, and the BAL outflow velocity and UV absorption strength are correlated with relative X-ray weakness. These results are in qualitative agreement with models that depend on strong X-ray absorption to shield the outflow from over-ionization and enable radiative acceleration....