The magnetism of the polyoxometalate cluster {Mo75V20}, containing a sawtooth ring of 10 corner-sharing triangles located on the equator of the barrel-shaped molecule, has remained debatable since it is masked by contributions from impurities as well as temperature-independent paramagnetism. In this article we demonstrate the usefulness of ESR measurements since the temperature dependence of the ESR intensity can discriminate between impurity and molecular contributions. We determine the exchange parameters and therefore also the low-lying spectrum of {Mo75V20}, especially the low-lying singlet states which so far have been probed solely by specific heat measurements. ; Comment: 5 pages, 5 figures, submitted to PRB