We present Far Ultraviolet Spectroscopic Explorer (FUSE) and Space Telescope Imaging Spectrograph (STIS E140M) observations of the post-asymptotic giant branch star ZNG 1 in the globular cluster Messier 5 (l=3.9, b=+47.7; d=7.5 kpc, z=+5.3 kpc). High velocity absorption is seen in C IV, Si IV, O VI, and lower ionization species at LSR velocities of -140 and -110 km/s. We conclude that this gas is not circumstellar on the basis of photoionization models and path length arguments. Thus, the high velocity gas along the ZNG 1 sight line is the first evidence that highly-ionized HVCs can be found near the Galactic disk. We measure the metallicity of these HVCs to be [O/H]=+0.22\pm0.10, the highest of any known HVC. Given the clouds' metallicity and distance constraints, we conclude that these HVCs have a Galactic origin. This sight line probes gas toward the inner Galaxy, and we discuss the possibility that these HVCs may be related to a Galactic nuclear wind or Galactic fountain circulation in the inner regions of the Milky Way.