  We propose Swampland constraints on consistent 5-dimensional ${\cal N}=1$
supergravity theories. We focus on a special class of BPS magnetic monopole
strings which arise in gravitational theories. The central charges and the
levels of current algebras of 2d CFTs on these strings can be calculated by
anomaly inflow mechanism and used to provide constraints on the low-energy
particle spectrum and the effective action of the 5d supergravity based on
unitarity of the worldsheet CFT. In M-theory, where these theories are realized
by compactification on Calabi-Yau 3-folds, the special monopole strings arise
from wrapped M5-branes on special ("semi-ample") 4-cycles in the threefold. We
identify various necessary geometric conditions for such cycles to lead to
requisite BPS strings and translate these into constraints on the low-energy
theories of gravity. These and other geometric conditions, some of which can be
related to unitarity constraints on the monopole worldsheet, are additional
candidates for Swampland constraints on 5-dimensional ${\cal N}=1$ supergravity
theories.
