  Let (M,{\eta},{\xi},{\Phi},g) be a compact quasi-regular Sasakian 5-manifold
with finite cyclic quotient foliation singularities of type (1/r)(1,a). First,
we derive the foliation minimal model program by applying the resolution of
cyclic quotient foliation singularities. Secondly, based on the study of local
model of resolution of foliation singularities, we prove the foliation
canonical surgical contraction or the foliation extremal ray contraction under
the Sasaki-Ricci flow. As a consequence, we prove a Sasaki analogue of analytic
minimal model program with the Keahler-Ricci flow due to Song-Tian and
Song-Weinkove.
