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We show how to construct the familiar heterotic NS5 brane as a topologicalsoliton in a supercritical version of heterotic string theory. Closed stringtachyon condensation removes the extra dimensions, leaving the NS5 in 10d, in aprocess highly reminiscent of the K-theoretical description of type IID-branes, but linking non-trivial gauge bundles and geometry. The constructionrequires a modification of the anomalous Bianchi identity for $H_3$ insupercritical heterotic string theory. We give various proofs for the existenceof this modification.

Heterotic NS5-branes from closed string tachyon condensation