We investigate the CO excitation of normal (near-IR selected BzK) star-forming (SF) disk galaxies at z = 1.5 using IRAM Plateau de Bure observations of the CO[2-1], CO[3-2], and CO[5-4] transitions for four galaxies, including VLA observations of CO[1-0] for three of them, with the aim of constraining the average state of H-2 gas. By exploiting previous knowledge of the velocity range, spatial extent, and size of the CO emission, we measure reliable line fluxes with a signal-to-noise ratio > 4-7 for individual transitions. While the average CO spectral line energy distribution (SLED) has a subthermal excitation similar to the Milky Way (MW) up to CO[3-2], we show that the average CO[5-4] emission is four times stronger than assuming MW excitation. This demonstrates that there is an additional component of more excited, denser, and possibly warmer molecular gas. The ratio of CO[5-4] to lower-J CO emission is lower than in local (ultra-)luminous infrared galaxies (ULIRGs) and high-redshift starbursting submillimeter galaxies, however, and appears to be closely correlated with the average intensity of the radiation field < U > and with the star formation surface density, but not with the star formation efficiency. The luminosity of the CO[5-4] transition is found to be linearly correlated with the bolometric infrared luminosity over four orders of magnitudes. For this transition, z = 1.5 BzK galaxies follow the same linear trend as local spirals and (U)LIRGs and high-redshift star-bursting submillimeter galaxies. The CO[5-4] luminosity is thus empirically related to the dense gas and might be a more convenient way to probe it than standard high-density tracers that are much fainter than CO. We see excitation variations among our sample galaxies that can be linked to their evolutionary state and clumpiness in optical rest-frame images. In one galaxy we see spatially resolved excitation variations, where the more highly excited part of the galaxy corresponds to the location of massive SF clumps. This provides support to models that suggest that giant clumps are the main source of the high-excitation CO emission in high-redshift disk-like galaxies.