  We construct supersymmetric gravitational soliton solutions of
five-dimensional gauged supergravity coupled to arbitrarily many vector
multiplets. The solutions are complete, globally stationary, $1/4$-BPS and are
asymptotically locally AdS$_5$ with conformal boundary $\mathbb{R} \times
L(p,1)$. The construction uses an $SU(2) \times U(1)-$invariant ansatz
originally used by Gutowski and Reall to construct supersymmetric
asymptotically AdS$_5$ black holes. A subset of these solutions have previously
been obtained as supersymmetric limits of a class of local solutions of
$U(1)^3$ gauged supergravity found by Chong-Cvetic-Lu-Pope, and by
Lucietti-Ovchinnikov in their classification of $SU(2)$-invariant solutions of
minimal gauged supergravity.
