© 2015. The American Astronomical Society. All rights reserved. We present new Very Large Array (VLA) H I spectral line imaging of five sources discovered by the ALFALFA extragalactic survey. These targets are drawn from a larger sample of systems that were not uniquely identified with optical counterparts during ALFALFA processing, and as such have unusually high H I mass to light ratios. The candidate "Almost Dark" objects fall into four broad categories: (1) objects with nearby H I neighbors that are likely of tidal origin; (2) objects that appear to be part of a system of multiple H I sources, but which may not be tidal in origin; (3) objects isolated from nearby ALFALFA H I detections, but located near a gas-poor early type galaxy; (4) apparently isolated sources, with no object of coincident redshift within ∼400 kpc. Roughly 75% of the 200 objects without identified counterparts in the α.40 database (Haynes et al. 2011) fall into category 1 (likely tidal), and were not considered for synthesis follow-up observations. The pilot sample presented here (AGC193953, AGC208602, AGC208399, AGC226178, and AGC233638) contains the first five sources observed as part of a larger effort to characterize H I sources with no readily identifiable optical counterpart at single dish resolution (3′.5). These objects span a range of H I mass [7.41 <log (MHI) <9.51] and H I mass to B-band luminosity ratios (3 <MHI/LB <9). We compare the H I total intensity and velocity fields to optical imaging drawn from the Sloan Digital Sky Survey and to ultraviolet imaging drawn from archival GALEX observations. Four of the sources with uncertain or no optical counterpart in the ALFALFA data are identified with low surface brightness optical counterparts in Sloan Digital Sky Survey imaging when compared with VLA H I intensity maps, and appear to be galaxies with clear signs of ordered rotation in the H I velocity fields. Three of these are detected in far-ultraviolet GALEX images, a likely indication of star formation within the last few hundred Myrs. One source (AGC208602) is likely tidal in nature, associated with the NGC 3370 group. Consistent with previous efforts, we find no "dark galaxies" in this limited sample. However, the present observations do reveal complex sources with suppressed star formation, highlighting both the observational difficulties and the necessity of synthesis follow-up observations to understand these extreme objects.