  We construct supersymmetric completions of various curvature squared terms in
five dimensional supergravity with eight supercharges. Adopting the dilaton
Weyl multiplet, we obtain the minimal off-shell supersymmetric Ricci scalar
squared as well as all vector multiplets coupled curvature squared invariants.
Since the minimal off-shell supersymmetric Riemann tensor squared and
Gauss-Bonnet combination in the dilaton Weyl multiplet have been obtained
before, both the minimal off-shell and the vector multiplets coupled curvature
squared invariants in the dilation Weyl multiplet are complete. We also
constructed an off-shell Ricci scalar squared invariant utilizing the standard
Weyl multiplet. The supersymmetric Ricci scalar squared in the standard Weyl
multiplet is coupled to n number of vector multiplets by construction, and it
deforms the very special geometry. We found that in the supersymmetric AdS_5
vacuum, the very special geometry defined on the moduli space is modified in a
simple way. Finally, we study the magnetic string and electric black hole
solutions in the presence of supersymmetric Ricci scalar squared.
