The ultra-faint dwarf galaxy Leo V has shown both photometric overdensities and kinematic members at large radii, along with a tentative kinematic gradient, suggesting that it may have undergone a close encounter with the Milky Way. We investigate these signs of disruption through a combination of (I) high precision photometry obtained with the Hubble Space Telescope (HST), (II) two epochs of stellar spectra obtained with the Hectochelle Spectrograph on the MMT, and (III) measurements from the Gaia mission. Using the HST data, we examine one of the reported stream-like overdensities at large radii, and conclude that it is not a true stellar stream, but instead a clump of foreground stars and background galaxies. Our spectroscopic analysis shows that one known member star is likely a binary, and challenges the membership status of three others, including two distant candidates that had formerly provided evidence for overall stellar mass loss. We also find evidence that the proposed kinematic gradient across Leo V might be due to small number statistics. We update the systemic proper motion of Leo V, finding ({mu}_{alpha}_/cos{delta},{mu}_{delta}_)= (0.009{+/-}0.560,-0.777{+/-}0 .314)mas/yr, which is consistent with its reported orbit that did not put Leo V at risk of being disturbed by the Milky Way. These findings remove most of the observational clues that suggested Leo V was disrupting; however, we also find new plausible member stars, two of which are located >5 half-light radii from the main body. These stars require further investigation. Therefore, the nature of Leo V still remains an open question.