Abstarct: The basis of the cluster model is baxsed on the principle that within the nuclei there are combinations of nucleons that interact with each other while maintain themselves. A cluster model is one of the most efficient nuclear models in describing multi-body systems. Investigating the characteristics of five-body systems due to having 15 degrees of freedom is very complicated and difficult; one of the useful ways for solving this problem is using a cluster model. In this model, the five-particle system is converted into two-particle systems or three-particle systems. Instead of investigating the interactions of individual particles, we check interactions between each cluster and determine the properties of the system, considering the suitable potential as interaction between clusters. Five-nucleon systems (nuclei that have five nucleons out of closed shell, In the nuclear structure, the shell with the highest number of nucleons allowed by the exclusion principle is called a closed shell.) and five-quark systems (Pentaquarks) are two examples of five-body systems. Pentaquark is an exotic hadron with five quark that it can be modeled such as diquark-triquark structure or diquark-diquark-antiquark structure in cluster model. Mirror nuclei, like 9B and 9Be, due to their nucleon placement at nuclear levels, can be modeled in different ways. One of the cluster models for these nuclei is the α-α-n and α-α-p structure. In this thesis, by solving an independent Schrödinger time equation for the studied nuclei, by suitable potentials for interaction between particles, the energy value and the 9Be and 9B wave function have been calculated in both shell and cluster models using the parametric method of NU. We have obtained acceptable results in comparison with experimental values. Using the cluster model (diquark-triquark) for Pentaquark , we have calculated the energy and the wave function of it in the non-relativistic approach in the presence of modified Yukawa potential. Also, we have calculated the energy levels and wave function of 21Na and 21Ne. Finally, we have calculated the energy values of the mentioned nuclei in the relativistic system by considering them as a double magic core with single nucleon around it in cluster structure by solving the Dirac equation using the PNU method and obtained acceptable results compared to the experimental results.