A five-dimensional (5D) APSY (automated projection spectroscopy) HCNCH experiment is presented, which allows unambiguous correlation of sugar to base nuclei in nucleic acids. The pulse sequence uses multiple quantum (MQ) evolution which enables long constant-time evolution periods in all dimensions, an improvement that can also benefit non-APSY applications. Applied with an RNA with 23 nucleotides the 5D APSY-HCNCH experiment produced a complete and highly precise 5D chemical shift list within 1.5 h. Alternatively, and for molecules where the out-and-stay 5D experiment sensitivity is not sufficient, a set of out-and-back 3D APSY-HCN experiments is proposed: an intra-base (3D APSY-b-HCN) experiment in an MQ or in a TROSY version, and an MQ sugar-to-base (3D APSY-s-HCN) experiment. The two 3D peak lists require subsequent matching via the N1/9 chemical shift values to one 5D peak list. Optimization of the 3D APSY experiments for maximal precision in the N1/9 dimension allowed matching of all ¹⁵N chemical shift values contained in both 3D peak lists. The precise 5D chemical shift correlation lists resulting from the 5D experiment or a pair of 3D experiments also provide a valuable basis for subsequent connection to chemical shifts derived with other experiments.