  Generic heterotic M-theory compactifications contain five-branes wrapping
non-isolated genus zero or higher genus curves in a Calabi-Yau threefold.
Non-perturbative superpotentials do not depend on moduli of such five-branes.We
show that fluxes and non-perturbative effects can stabilize them in a
non-supersymmetric AdS vacuum. We also show that these five-branes can be
stabilized in a dS vacuum, if we modify the supergravity potential energy by
Fayet-Iliopoulos terms. This allows us to stabilize all heterotic M-theory
moduli in a dS vacuum in the most general compactification scenarios. In
addition, we demonstrate that, by this modification, one can create an
inflationary potential. The inflationary phase is represented by a five-brane
approaching the visible brane. We give a qualitative argument how extra states
becoming light, when the five-brane comes too close, can terminate inflation.
Eventually, the five-brane hits the visible brane and disappears through a
small instanton transition. The post-inflationary system of moduli has simpler
stability properties. It can be stabilized in a dS vacuum with a small
cosmological constant.
