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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 theirorbits in the co-adjoint representation (K-orbits) are orbits of zero ormaximal dimension. The main result of the paper is the classification up to anisomorphism of all MD5-algebras with the non-commutative derived ideal. Withthis result, we have the complete classification of 5-dimensional solvable Liealgebras.

Classification of 5-Dimensional MD-Algebras Having Non-Commutative Derived Ideals