International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2641 2020 2020 Applied Science Private University Amman,11931, Jordan Abdallah Abdallah Department of Computer Information Systems, The University of Jordan – Aqaba, Jordan Ahmed Atallah Alsaraireh Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan Malik Bataineh Department of Mathematics, Jerash University, Jerash, Jordan Nabeela Abu Abu-Alkishik Department of Mathematics, Faculty of Sciences, University of Jordan, Amman 11942, Jordan Isra Al Al-Shbeil Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan Abdallah Al Al-Husban This paper will study the necessary conditions and sufficient conditions for the problem of orthogonality in 4-plithogenic and 5-plithogenic vector spaces, where we provided a definition of the real scalar products defined above these spaces, and we used the new concept of scalar product that was defined in determining the necessary and sufficient condition for the orthogonality of symbolic 4-plithogenic and 5-plithogenic vectors, in addition to calculating various norms and their metric properties. We have also provided some examples that aim to explain the scientific contribution of this work. 2024 2024 94 103 10.54216/IJNS.240109 https://www.americaspg.com/articleinfo/21/show/2641