The nature and origin of the high-velocity clouds (HVCs) of neutral hydrogen in our Galaxy are not well understood, in part because of the uncertain distances to the clouds. As a result it is difficult to measure the mass of neutral hydrogen in the HVCs in the Galaxy, but further insight into the nature of HVCs can be obtained by finding and studying such gas in other galaxies. The Sc-galaxy NGC 5668 was found to have high-velocity wings beyond the double-horned 21 cm profile in observations performed with the Arecibo 305 m telescope; these wings are the expected signature of HVCs in a disk galaxy. In this paper, Very Large Array observations of NGC 5668 are presented that confirm the high- velocity H I wings detected with the Arecibo telescope. About 60% of the material in the high-velocity wings is distinct in position-velocity diagrams, located primarily outside the optical disk of the galaxy, and may be infalling material comparable to the Magellanic Stream in our own Galaxy. The total mass of this kinematically distinct neutral hydrogen is 4 x 10^8^ M_sun_. A natural source for the rest of the wing material is halo gas produced by a galactic fountain. Such a fountain would be driven by supernovae and energetic stellar winds from massive stars in OB associations that would also transfer kinetic energy to the neutral hydrogen disk. This would result in a larger H I velocity dispersion within the optical disk than outside of it, as is suggested by these observations.