  Recently a description of linearized 5D supergravity in 4D, N =1 superspace
was presented. By analyzing the on-shell component Lagrangian, this description
was proven to be Lorentz invariant in five dimensions. This paper describes a
geometric formulation of the 5D supergravity in 4D, N =1 superspace. Using this
new formalism, the on-shell structure of the previous description is verified
from purely superspace methods. This geometric description provides a
connection to dimensionally reduced manifestly supersymmetric 5D supergravity.
