  We investigate the hidden symmetries and existence of Killing spinors of D=5
minimal gauged supergravity solutions which admit a Killing-Maxwell system in
the sense of Carter, such as the Chong-Cveti$\check{c}$-L\"{u}-Pope (CCLP)
Kerr-dS black hole spacetime and a 5-dimensional minimal gauged supergravity
solution endowed with a Sasaki structure deformed by torsion, a limiting case
of the generalization of the 5-dimensional toric Sasaki-Einstein $L^{a,b,c}$
spacetime. We note that when an electromagnetic tensor is present and an
associated Killing-Maxwell system can be constructed in the sense of Carter,
the Killing-Maxwell field becomes a PCKY (principal conformal Killing-Yano)
tensor or a PGCKY (principal generalized conformal Killing-Yano) tensor, the
latter in the presence of torsion. We find some new hidden symmetries of the
Chong-Cveti$\check{c}$-L\"{u}-Pope black hole, i.e. we construct two more
generalized St\"ackel-Killing tensors and the associated generalized
Killing-Yano (GKY) tensors. We also explicitly construct a Killing spinor for
the specific 5 dimensional minimal gauged supergravity solution that is endowed
with a Sasaki structure deformed by torsion mentioned above.
