  We construct new solutions of the Einstein equations with negative
cosmological constant in five spacetime dimensions. They smoothly emerge as
deformations of the known AdS$_5$ black strings. The first type of
configurations can be viewed as the $d=4$ Taub-NUT-AdS solutions uplifted to
five dimensions, in the presence of a negative cosmological constant. We argue
that these solutions provide the gravity dual for a ${\cal N}=4$
super-Yang-Mills theory formulated in a $d=4$ homogeneous G\"odel-type
spacetime background. A different deformation of the AdS$_5$ black strings
leads to squashed AdS black holes and their topological generalizations. In
this case, the conformal infinity is the product of time and a circle-fibration
over a base space that is a two-dimensional Einstein space.
