Ruling out certain 5-spectra with one repeated eigenvalue for the symmetric NIEP

Abstract Here, prior work, that ruled out certain spectra with two repeated eigenvalues for the 5-by-5 S-NIEP, is extended. Previously unresolved spectra with just one repeated eigenvalue are shown not to occur. The repeat could be either positive or negative, but the two situations are different. In both situations, the prior result with two repeats is a special case.