2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60649In this paper we consider the problem of classifying the $(n-5)$-filiform Lie algebras. This is the first index for which infinite parametrized families appear, as can be seen in dimension $7.$ Moreover we obtain large families of characteristic nilpotent Lie algebras with nilpotence index 5 and show that at least for dimension 10 there is a characteristic nilpotent Lie algebra with nilpotence index 4 which is the algebra of derivations of a nilpotent Lie algebra.30 pages, 9 tables. Tables 8 and 9 should be printed horizontallyRings and Algebras17B30text