  We present high-resolution (0.17\arcsec $\times$ 0.14\arcsec) Atacama Large
Millimeter/submillimeter Array (ALMA) observations of the CO\,(6-5) line, and
435\um\ dust continuum emission within a $\sim$9\arcsec $\times$ 9\arcsec\ area
centered on the nucleus of the galaxy NGC\,5135. NGC\,5135 is a well-studied
luminous infrared galaxy that also harbors a Compton-thick active galactic
nucleus (AGN). At the achieved resolution of 48 $\times$ 40\,pc, the CO\,(6-5)
and dust emissions are resolved into gas "clumps" along the symmetrical dust
lanes associated with the inner stellar bar. The clumps have radii between
$\sim$45-180\,pc and CO\,(6-5) line widths of $\sim$60-88\,\kms. The CO\,(6-5)
to dust continuum flux ratios vary among the clumps and show an increasing
trend with the \FeII/Br-$\gamma$ ratios, which we interpret as evidence for
supernova-driven shocked gas providing a significant contribution to the \co65\
emission. The central AGN is undetected in continuum, nor in CO\,(6-5) if its
line velocity width is no less than $\sim$\,40\,\kms. We estimate that the AGN
contributes at most 1\% of the integrated CO\,(6-5) flux of 512 $\pm$
24$\,$Jy\kms\ within the ALMA field of view, which in turn accounts for
$\sim$32\% of the CO\,(6-5) flux of the whole galaxy.
