  Given a nilpotent Lie algebra, we study the space of all diagonalizable
derivations such that the corresponding one-dimensional solvable extension
admits a left-invariant metric with negative Ricci curvature. It has been
conjectured by Lauret-Will that such a space coincides with an open and convex
subset of derivations defined in terms of the moment map for the variety of
nilpotent Lie algebras. We prove the validity of the conjecture in dimension 5,
as well as for Heisenberg and standard filiform Lie algebras.
