The fourth edition of the Sloan Digital Sky Survey (SDSS) Quasar Catalog, made from the SDSS Fifth Data Release, contains 77,429 objects; this is an increase of over 30,000 entries since the previous edition (Schneider et al., Cat. <VII/243>). The catalog consists of the objects in the SDSS Fifth Data Release that have luminosities larger than M_i_=-22.0 (in a cosmology with Ho=70km.s-1.Mpc-1, {Omega}_M_=0.3, and {Omega}_{Lambda}_=0.7), have at least one emission line with FWHM larger than 1000km.s-1 or have interesting or complex absorption features, are fainter than i~15.0, and have highly reliable redshifts. The area covered by the catalog is about 5740deg^2^. The quasar redshifts range from 0.08 to 5.41, with a median value of 1.48; the catalog includes 891 quasars at redshifts greater than 4, of which 36 are at redshifts greater than 5. Approximately half of the catalog quasars have i<19; nearly all have i<21. For each object the catalog presents positions accurate to better than 0.2" rms per coordinate, five-band (ugriz) CCD-based photometry with typical accuracy of 0.03mag, and information on the morphology and selection method. The catalog also contains basic radio, near-infrared, and X-ray emission properties of the quasars, when available, from other large-area surveys. The calibrated digital spectra cover the wavelength region 3800-9200{AA} at a spectral resolution of about 2000; the spectra can be retrieved from the public database using the information provided in the catalog. The average SDSS colors of quasars as a function of redshift, derived from the catalog entries, are presented in tabular form. Approximately 96% of the objects in the catalog were discovered by the SDSS.