  All five-dimensional non-abelian gauge theories have a $U(1)_I$ global
symmetry associated with instantonic particles. We describe an obstruction to
coupling $U(1)_I$ to a classical background gauge field that occurs whenever
the theory has a one-form center symmetry. This is a finite-order mixed 't
Hooft anomaly between the two symmetries. We also show that a similar
obstruction takes place in gauge theories with fundamental matter by studying
twisted bundles for the ordinary flavor symmetry. We explore some general
dynamical properties of the candidate phases implied by the anomaly. Finally,
we apply our results to supersymmetric gauge theories in five dimensions and
analyze the symmetry enhancement patterns occurring at their conjectured RG
fixed points.
