  In this note we investigate certain topological aspects of the effective
action of the NS5-brane in type IIA string theory. To facilitate the study of
the corresponding partition function, we define a cohomology class whose
vanishing is a necessary condition for this function to be well-defined. This
leads to various topological conditions, including a twisted Fivebrane
structure as well as secondary cohomology operations arising from a K-theoretic
description. We explain how these operations also generate the topological part
of the action as well as the phase of the partition function. Part of the
discussion also applies to the M5-brane.
