  We study freely acting orbifolds of type IIB string theory on $T^5$ that
spontaneously break supersymmetry from $\mathcal{N}=8$ to $\mathcal{N}=6,4,2$
or 0 in five dimensions. We focus on orbifolds that are a $\mathbb{Z}_p$
quotient by a T-duality acting on $T^4$ and a shift on the remaining $S^1$.
Modular invariant partition functions are constructed and detailed examples of
both symmetric and asymmetric orbifolds are presented, including new examples
of five-dimensional non-supersymmetric string theories with no tachyons. The
orbifolds we consider arise at special points in the moduli space of string
theory compactifications with a duality twist. The supergravity limit of these
are Scherk-Schwarz reductions which generate gauged supergravities with
positive definite potentials on the moduli space in five dimensions. Both
symmetric and asymmetric freely acting orbifolds give a landscape of Minkowski
vacua. For gauged supergravities to belong to this landscape, we find a number
of constraints and conditions. Firstly, the scalar potential should lead to a
massive spectrum with masses that obey quantization conditions arising from a
string theory orbifold, which we discuss in detail. Secondly, we find
constraints on the massless sector, e.g. in the examples of orbifolds
preserving sixteen supercharges in five dimensions that we consider, only an
odd number of vector multiplets arise. Lastly, we present new examples of
candidate asymmetric orbifolds with modular invariant partition functions, but
with non-integral coefficients in the $q\bar{q}$-expansion in the twisted
sector.
