The most stable forms of E5Li7+ (E=Ge, Sn, and Pb) have been explored by means of a stochastic search of their potential-energy surfaces by using the gradient embedded genetic algorithm (GEGA). The preferred isomer of the Ge5Li7+ ion is a slightly distorted analogue of the D5h three-dimensional seven-pointed starlike structure adopted by the lighter C5Li7+ and Si5Li7+ clusters. In contrast, the preferred structures for Sn5Li7+ and Pb5Li7+ are quite different. By starting from the starlike arrangement, corresponding lowest-energy structures are generated by migration of one of the E atoms out of the plane with the a corresponding rearrangement of the Li atoms. To understand these structural preferences, we propose a new energy decomposition analysis based on isomerizations (isomerization energy decomposition analysis (IEDA)), which enable us to extract energetic information from isomerization between structures, mainly from highly charged fragments.