  We present an extended study of our previous work on an alternative
five-dimensional N=2 supergravity theory that has a single antisymmetric tensor
and a dilaton as a part of supergravity multiplet. The new fields are natural
Neveu-Schwarz massless fields in superstring theory. Our total matter
multiplets include n copies of vector multiplets forming the sigma-model coset
space SO(n,1) / SO(n), and n' copies of hypermultiplets forming the
quaternionic K\"ahler manifold Sp(n',1) / Sp(n') X Sp(1). We complete the
couplings of matter multiplets to supergravity with the gauged group of the
type SO(2) X Sp(n') X Sp(1) X H X [ U(1) ]^{n-p+1} for an arbitrary gauge group
H with p = dim H + 1, and the isotropy group Sp(n') X Sp(1) of the coset
Sp(n',1) / Sp(n') X Sp(1) formed by the hypermultiplets. We also describe the
generalization to singular 5D space-time as in the conventional formulation
