  There are studied in details 5-dimensional pseudo-Riemannian manifolds
equipped with the structure analogous to the almost cosymplectic (almost
coKaehler) structure. The curvature by assumption commutes with the structure
affinor and all these manifolds are Walker spaces. There are obtained
classifications for manifolds for contact Ricci potential, locally flat
manifolds and described all connected, simply connected Lie groups admiting
left-invariant structure. There are some other more general results.
