AdS_5 Supersymmetry in N=1 Superspace

We use N=1 superspace to construct the supersymmetric matter couplings of vector and hyper multiplets in a five-dimensional anti-de Sitter spacetime background. For hypermultiplets, we find that AdS_5 supersymmetry requires the scalar fields to lie on a hyper-Kahler manifold endowed with a certain type of holomorphic Killing vector.