We have observed the much-studied Seyfert 1 galaxy NGC 5548 with the Goddard High-Resolution Spectrograph (GHRS) on the Hubble Space Telescope (HST). Our 14 ks observation covers the C IV emission line at a resolution of greater than 20,000. Our purpose was to study the absorption line found at lower resolution by IUE and the HST Faint Object Spectrograph. We found that the C IV absorption line resolves into six separate doublets with equivalent widths of 0.07-0.38 Angstrom. The absorption lines have blueshifts relative to the systemic velocity of the galaxy of 380-1250 km s(-1), except for one, which has a redshift of 250 km s(-1), suggesting both inflow and outflow. The inflowing component may be related to the accretion flow into the nuclear black hole. All the doublet lines are resolved by the GHRS. Three doublets are narrow, with FWHM less than or similar to 100 km s(-1), and three are broad, FWHM similar to 160-290 km s(-1). We find evidence of partial covering by the narrow absorption lines. Either (but not both) of the two strongest broad doublets could be from the same material that produces the X-ray ionized absorber seen in soft X-rays. The remaining five systems must be at least 10 times less ionized (and so of lower total column density) to remain consistent with the X-ray spectra.