In this paper, we compute the minimum discriminants of imprimitive degree-10 fields for different combinations of Galois group and signature. We use class field theory when there is a quintic subfield, and a Martinet search in the more difficult case in which there is only a quadratic subfield.
"Minimum Discriminants of Imprimitive Decic Fields." Experiment. Math. 19 (4) 475 - 479, 2010.