Unstable 5D spacetime?

One of the thought-provoking things that M.K. mentioned was a paper about

• a Witten bubble-like instanton

in 5 dimensions without any Kaluza-Klein compactification. The solution is inspired by the black rings. If the solution and its interpretation were true, spacetimes with five dimensions would be unstable. Of course, it can't be true for supersymmetric spacetimes. But in his construction, there seems to be no obstruction on the spin structure, like the obstruction that tells you that only the Scherk-Schwarz compactification suffers from the Witten bubble instability. If someone knows what are the answers to these simple but puzzling questions, please, let me know.