Intrinsically disordered proteins (IDPs) have recently attracted much interest, due to their role in many biological processes, including signaling and regulation mechanisms. High-dimensional (13)C direct-detected NMR experiments have proven exceptionally useful in case of IDPs, providing spectra with superior peak dispersion. Here, two such novel experiments recorded with non-uniform sampling are introduced, these are 5D HabCabCO(CA)NCO and 5D HNCO(CA)NCO. Together with the 4D (HACA)CON(CA)NCO, an extension of the previously published 3D experiments (Pantoja-Uceda and Santoro in J Biomol NMR 59:43-50, 2014. doi: 10.1007/s10858-014-9827-1), they form a set allowing for complete and reliable resonance assignment of difficult IDPs. The processing is performed with sparse multidimensional Fourier transform based on the concept of restricting (fixing) some of spectral dimensions to a priori known resonance frequencies. In our study, a multiple-fixing method was developed, that allows easy access to spectral data. The experiments were tested on a resolution-demanding alpha-synuclein sample. Due to superior peak dispersion in high-dimensional spectrum and availability of the sequential connectivities between four consecutive residues, the overwhelming majority of resonances could be assigned automatically using the TSAR program.