  The Emergent String Conjecture of Lee, Lerche, and Weigand holds that every
infinite-distance limit in the moduli space of a quantum gravity represents
either a decompactification limit or an emergent string limit in some duality
frame. Within the context of 5d supergravities coming from M-theory
compactifications on Calabi-Yau threefolds, we find evidence for this
conjecture by studying (a) the gauge couplings and (b) the BPS spectrum, which
is encoded in the Gopakumar-Vafa invariants of the threefold. In the process,
we disuss a testable geometric consequence of the Emergent String Conjecture,
and we verify that it is satisfied in all complete intersection Calabi-Yau
threefolds in products of projective spaces (CICYs).
