We present the detection of CO (5−4) with signal-to-noise ratio (S/N) > 7-13 and a lower CO transition with S/N > 3 (CO (4−3) for four galaxies, and CO (3−2) for one) with the Atacama Large Millimeter/submillimeter Array in bands 3 and 4 in five main-sequence (MS) star-forming galaxies with stellar masses (3-6) × 1010M at 3 < z < 3.5. We find a good correlation between the total far-infrared luminosity LFIR and the luminosity of the CO (5−4) transition , where increases with star formation rate (SFR), indicating that CO (5−4) is a good tracer of the obscured SFR in these galaxies. The two galaxies that lie closer to the star-forming MS have CO spectral line energy distribution (SLED) slopes that are comparable to other star-forming populations, such as local submillimeter galaxies and BzK star-forming galaxies; the three objects with higher specific star formation rates have far steeper CO SLEDs, which possibly indicates a more concentrated episode of star formation. By exploiting the CO SLED slopes to extrapolate the luminosity of the CO (1−0) transition and using a classical conversion factor for MS galaxies of , we find that these galaxies are very gas-rich, with molecular gas fractions between 60% and 80% and quite long depletion times, between 0.2 and 1 Gyr. Finally, we obtain dynamical masses that are comparable to the sum of stellar and gas mass (at least for four out of five galaxies), allowing us to put a first constraint on the CO parameter for MS galaxies at an unprecedented redshift.