We tabulate velocities and other parameters of hydrogen recombination lines near 5GHz (H109{alpha} and H110{alpha}) for 316 HII regions observed with the Parkes 64-m radio telescope. Results of a new search for formaldehyde absorption are also listed. Source selection was based on the 5GHz continuum southern galactic plane survey of Haynes et al. (1978, 1979). Data is given for most H II regions in the galactic longitude range 210 to 360 degrees that show 5GHz continuum brightness temperature exceeding 1K (as observed with the 4 arcminute beam of the Parkes 64-m telescope), together with a selection of sources that are weaker or outside of this longitude range. Tabulated data include source coordinates, peak brightness, flux density, and angular size from the 5GHz continuum survey; radial velocities of detected formaldehyde absorption lines; recombination line peak brightness, radial velocity, and line width; derived electron temperature assuming LTE; derived kinematic distance from the Sun and galactocentric radius; and presence or absence of a visible optical counterpart. In cases where kinematic distance is ambiguous, both near and far distances are tabulated; a flag is given if there is a strong preference for near or far distance based on information such as H I or H2CO absorption measurements or visibility of an optical counterpart. Many of these radio HII regions lie beyond the range of optical detection, at distances exceeding several kpc; they thus provide a comprehensive coverage of the southern HII regions in the Galaxy over the longitude range 210 to 360 degrees and constitute a vital data base for the study of galactic structure.