  Using the sharpened Helgason-Johnson bound, this paper classifies all the
irreducible unitary representations with non-zero Dirac cohomology of
$E_{7(-5)}$. As an application, we find that the cancellation between the even
part and the odd part of the Dirac cohomology continues to happen for certain
unitary representations of $E_{7(-5)}$. Assuming the infinitesimal character
being integral, we further improve the Helgason-Johnson bound for $E_{7(-5)}$.
This should help people to understand (part of) the unitary dual of this group.
