  An off-shell formulation of two distinct tensor multiplets,a massive tensor
multiplet and a tensor gauge multiplet, is presented in superconformal tensor
calculus in five-dimensional space-time. Both contain a rank 2 antisymmetric
tensor field, but there is no gauge symmetry in the former, while it is a gauge
field in the latter. Both multiplets commonly have 4 bosonic and 4 fermionic
{\em on-shell} modes, but the former consists of 16(boson)+16(fermion)
component fields while the latter consists of 8(boson)+8(fermion) component
fields.
