  Using the superspace formulation for the 5D N = 1 Weyl supermultiplet
developed in arXiv:0802.3953, we elaborate the concept of conformally flat
superspace in five dimensions. For a large family of supersymmetric theories
(including sigma-models and Yang-Mills theories) in the conformally flat
superspace, we describe an explicit procedure to formulate their dynamics in
terms of rigid 4D N = 1 superfields. The case of 5D N = 1 anti-de Sitter
superspace is discussed as an example.
