We present our high-resolution (0."15 x 0."13, similar to 34pc) observations of the CO (6-5) line emission, which probes the warm and dense molecular gas, and the 434 mu m dust continuum emission in the nuclear region of the starburst galaxy IC 5179, conducted with the Atacama Large Millimeter Array (ALMA). The CO. (6-5) emission is spatially distributed in filamentary structures with many dense cores and shows a velocity field that is characteristic of a circumnuclear rotating gas disk, with 90% of the rotation speed arising within a radius of less than or similar to 150 pc. At the scale of our spatial resolution, the CO. (6-5) and dust emission peaks do not always coincide, with their surface brightness ratio varying by a factor of similar to 10. This result suggests that their excitation mechanisms are likely different, as further evidenced by the southwest to northeast spatial gradient of both CO-to-dust continuum ratio and Pa-alpha equivalent width. Within the nuclear region (radius similar to 300 pc) and with a resolution of similar to 34 pc, the CO line flux (dust flux density) detected in our ALMA observations is 180 +/- 18 Jy km s(-1) (71 +/- 7 mJy), which accounts for 22% (2.4%) of the total value measured by Herschel.