  Witten indices and partition functions are computed for abelian 6d tensor and
hypermultiplets on $\mathbb{R}\times S^5$ in Lorentzian signature in an R gauge
field background which preserves some supersymmetry. We consider a generic
supersymmetric squashing that also admits squashing of the Hopf fiber. Wick
rotation to Euclidean M5 brane amounts to Wick rotation of squashing parameters
and the hypermultiplet mass parameter. We compute Casimir energies for tensor
and hypermultiplets separately for general squashing, and match these with the
corresponding gravitational anomaly polynomials. We extract Witten indices on
$\mathbb{R}\times \mathbb{CP}^2$ and find that this is zero, again matching
with the vanishing anomaly polynomial on an odd dimensional space.
