  The paper presents a subclass of the class of MD5-algebras and MD5-groups,
i.e., five dimensional solvable Lie algebras and Lie groups such that their
orbits in the co-adjoint representation (K-orbit) are orbit of zero or maximal
dimension. The main results of the paper is the classification up to an
isomorphism of all MD5-algebras $\mathcal{G}$ with the derived ideal
${\mathcal{G}}^{1} := [\mathcal{G}, \mathcal{G}]$ is a 3-dimensional
commutative Lie algebra.
