Two novel 5D NMR experiments (CACONCACO, NCOCANCO) for backbone assignment of disordered proteins are presented. The pulse sequences exploit relaxation properties of the unstructured proteins and combine the advantages of 13C-direct detection, non-uniform sampling, and longitudinal relaxation optimization to maximize the achievable resolution and minimize the experimental time. The pulse sequences were successfully tested on the sample of partially disordered delta subunit from RNA polymerase from Bacillus subtilis. The unstructured part of this 20 kDa protein consists of 81 amino acids with frequent sequential repeats. A collection of 0.0003% of the data needed for a conventional experiment with linear sampling was sufficient to perform an unambiguous assignment of the disordered part of the protein from a single 5D spectrum.