International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2617 2020 2020 Mutah University, Faculty of Science, Mutah, Jordan Cuauhtemoc Cuauhtemoc College of Business Administration, American University of the Middle East, 54200, Egaila, Kuwait Cuauhtemoc Samaniego Tashkent State University of Economics, Uzbekistan Khakimova Khulkar Khamitovna The objective of this paper is to study for the first time the concept of symbolic 5-plithogenic vector space defined over symbolic 5-plithogenic field. Many results about the algebraic properties of this class of spaces will be obtained, where we define AH-subspaces, AH-linear transformations, and kernels. Also, we study the inner products defined over symbolic 5-plithogenic vector spaces and determine the conditions of orthogonality in these spaces with many interesting examples. 2024 2024 376 385 10.54216/IJNS.230430 https://www.americaspg.com/articleinfo/21/show/2617