| Summary: | In this paper, we present an exact analytical solution for five interacting quarks. We solve the Schr\"{o}dinger equation for pentaquarks in the framework of five-body and two-body problems. For this purpose, we utilize Yukawa potential in Jacobi coordinates. Also finding the relation between the reduced masses and coupling constants of pentaquarks, we obtain the coupling constant of Yukawa potential for pentaquark systems. We calculate the energy of these systems in their ground state. The results are well consistent with the theoretical results. Our procedure to obtain these results is appropriate for other potentials and $n$-body systems.
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