  Many black hole spacetimes with a 3-form field exhibit a hidden symmetry
encoded in a torsion generalization of the principal Killing--Yano tensor. This
tensor determines basic properties of such black holes while also underlying
the separability of the Hamilton--Jacobi, Klein--Gordon, and (torsion-modified)
Dirac field equations in their background. As a specific example, we consider
the Chong--Cveti\v{c}--L\"u--Pope black hole of $D=5$ minimal gauged
supergravity and show that the torsion-modified vector field equations can also
be separated, with the principal tensor playing a key role in the separability
ansatz. For comparison, separability of the Proca field in higher-dimensional
Kerr--NUT--AdS spacetimes (including new explicit formulae in odd dimensions)
is also presented.
