  In this paper, we derive the uniform L^{4}-bound of the transverse conic
Ricci curvature along the conic Sasaki-Ricci flow on a compact transverse log
Fano Sasakian manifold M of dimension five and the space of leaves of the
characteristic foliation is not well-formed. Then we first show that any
solution of the conic Sasaki-Ricci flow converges in the Cheeger-Gromov sense
to the unique singular orbifold conic Sasaki-Ricci soliton on M_{infinite}
which is a S^{1}-orbibundle over the unique singular conic Keahler-Ricci
soliton on a log del Pezzo orbifold surface. As a consequence, there exists a
Keahler-Ricci soliton orbifold metric on its leave space which is a log del
Pezzo orbifold surface. Second, we show that the conic Sasaki-Ricci soliton is
the conic Sasaki-Einstein if M is transverse log K-polystable. In summary, we
have the existence theorems of orbifold Sasaki-Ricci solitons and
Sasaki-Einstein metrics on a compact quasi-regular Sasakian manifold of
dimension five.
