  In this paper, we write down Seiberg-Witten equations on contact metric
manifolds of dimension 5. Any contact metric manifold has a spin^c structure.
For Dirac equation we use Dirac type operators associated to the generalized
Tanaka-Webster connection on spin^c spinor bundle of a contact metric manifold.
For curvature equation we need to self-duality concept. Self-duality concept is
significant on odd dimensional manifolds, particularly, on 5-dimensional
contact manifolds. Finally, we give a global solution to these equations on
strictly pseudoconvex CR manifolds.
