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In graph theory, lattices are used when some structural part of the graph repeats itself finitely or infinitely many times. They have applications in complex analysis and geometry in mathematics, and also natural applications in chemical graph theory. As a lattice can be taken as a graph, it is also possible to use them in the study of large networks. Recently, some topological graph indices of pentagonal chains is studied and here, we study some topological graph indices of pentagonal double chains similarly to that work. We make use of the vertex and edge partitions of these graphs and calculate their indices by means of these partitions and combinatorial methods.