  We study the rigid limit of 5d conformal supergravity with minimal
supersymmetry on Riemannian manifolds. The necessary and sufficient condition
for the existence of a solution is the existence of a conformal Killing vector.
Whenever a certain $SU(2)$ curvature becomes abelian the backgrounds define a
transversally holomorphic foliation. Subsequently we turn to the question under
which circumstances these backgrounds admit a kinetic Yang-Mills term in the
action of a vector multiplet. Here we find that the conformal Killing vector
has to be Killing. We supplement the discussion with various appendices.
