  We present the results of our calculations of the parity nonconserving
electric dipole amplitudes ($E1_{PNC}$) for the $6s ~ ^2S_{1/2} - 5d ~
^2D_{3/2;5/2}$ transitions of $^{133}$Cs employing a relativistic
coupled-cluster (RCC) method. $E1_{PNC}$ values for the nuclear spin
independent (NSI) and nuclear spin dependent (NSD) parity non-conservation
(PNC) effects for different hyperfine levels of the $6s ~ ^2S_{1/2} - 5d ~
^2D_{3/2}$ transition and only due to the NSD PNC interaction Hamiltonian for
all possible hyperfine levels of the $6s ~ ^2S_{1/2} - 5d ~ ^2D_{5/2}$
transition are given. We have also performed calculations of several properties
that are relevant for assessing the reliability of the calculations of the
amplitudes of the above mentioned transitions. We highlight the importance of
correlation effects by giving the results of both the Dirac-Fock (DF) and RCC
contributions. Approximate contributions to these properties from the Breit and
quantum electrodynamics (QED) interactions have also been evaluated. Plausible
experimental schemes to measure these transition amplitudes by light shift
techniques and interference involving induced Stark shifts are outlined.
