  In five-dimensional heterotic M-theory there is necessarily nonzero
background flux, which leads to gauging of an isometry of the universal
hypermultiplet moduli space. This isometry, however, is poised to be broken by
M5-brane instanton effects. We show that, similarly to string theory, the
background flux allows only brane instantons that preserve the above isometry.
The zero-mode counting for the M5 instantons is related to the number of
solutions of the Dirac equation on their worldvolume. We investigate that
equation in the presence of generic background flux and also, in a particular
case, with nonzero worldvolume flux.
