We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of high-J CO lines (J up = 6, 7, 8) and associated dust continuum toward five strongly lensed, dusty, star- forming galaxies at redshift z = 2.7-5.7. These galaxies, discovered in the South Pole Telescope survey, are observed at 0.″2-0.″4 resolution with ALMA. Our high-resolution imaging coupled with the lensing magnification provides a measurement of the structure and kinematics of molecular gas in the background galaxies with spatial resolutions down to kiloparsec scales. We derive visibility-based lens models for each galaxy, accurately reproducing observations of four of the galaxies. Of these four targets, three show clear velocity gradients, of which two are likely rotating disks. We find that the reconstructed region of CO emission is less concentrated than the region emitting dust continuum even for the moderate-excitation CO lines, similar to what has been seen in the literature for lower-excitation transitions. We find that the lensing magnification of a given source can vary by 20%-50% across the line profile, between the continuum and line, and between different CO transitions. We apply Large Velocity Gradient modeling using apparent and intrinsic line ratios between lower-J and high-J CO lines. Ignoring these magnification variations can bias the estimate of physical properties of interstellar medium of the galaxies. The magnitude of the bias varies from galaxy to galaxy and is not necessarily predictable without high-resolution observations.
