  We consider charged black holes with curved horizons, in five dimensional
dilaton gravity in the presence of Liouville-type potential for the dilaton
field. We show how, by solving a pair of coupled differential equations,
infinitesimally small angular momentum can be added to these static solutions
to obtain charged rotating dilaton black hole solutions. In the absence of
dilaton field, the non-rotating version of the solution reduces to the five
dimensional Reissner-Nordstr\"{o}m black hole, and the rotating version
reproduces the five dimensional Kerr-Newman modification thereof for small
rotation parameter. We also compute the angular momentum and the angular
velocity of these rotating black holes which appear at the first order.
