A method for five-dimensional spectral reconstruction of non-uniformly sampled NMR data sets is proposed. It is derived from the previously published signal separation algorithm, with major alterations to avoid unfeasible processing of an entire five-dimensional spectrum. The proposed method allows credible reconstruction of spectra from as little as a few hundred data points and enables sensitive resonance detection in experiments with a high dynamic range of peak intensities. The efficiency of the method is demonstrated on two high-resolution spectra for rapid sequential assignment of intrinsically disordered proteins, namely 5D HN(CA)CONH and 5D (HACA)CON(CO)CONH..