  The existing reservoirs of neutral atomic hydrogen gas (H$\,$I) in galaxies
are insufficient to have maintained the observed levels of star formation
without some kind of replenishment. {This refuelling of the H$\,$I reservoirs}
is likely to occur at column densities an order of magnitude lower than
previous observational limits (N$_{\rm{H\,I}\, limit} \sim 10^{19}\,$cm$^{-2}$
at 30$''$ resolution over a linewidth of $20\,$km/s). In this paper, we present
recent deep H$\,$I observations of NGC 5068, a nearby isolated star-forming
galaxy observed by MeerKAT as part of the MHONGOOSE survey. With these new
data, we are able to detect low column density H$\,$I around NGC 5068 with a
$3\sigma$ detection limit of N$_{\rm{H\,I}} = 6.4 \times 10^{17}\,$cm$^{-2}$ at
90$''$ resolution over a $20\,$km/s linewidth. The high sensitivity and
resolution of the MeerKAT data reveal a complex morphology of the H$\,$I in
this galaxy -- a regularly rotating inner disk coincident with the main
star-forming disk of the galaxy, a warped outer disk of low column density gas
(N$_{\rm{H\,I}} < 9 \times 10^{19}\,$cm$^{-2}$), in addition to clumps of gas
on the north west side of the galaxy. We employ a simple two disk model that
describe the inner and outer disks, and are able to identify anomalous gas that
deviates from the rotation of the main galaxy. The morphology and the
kinematics of the anomalous gas suggest a possible extra-galactic origin. We
explore a number of possible origin scenarios that may explain the anomalous
gas, and conclude that fresh accretion is the most likely scenario.
