aspg-21-2641-1791475980 20261008161300 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 1 Mayada Abualhomos Applied Science Private University Amman,11931, Jordan Ahmed Atallah Alsaraireh Department of Computer Information Systems, The University of Jordan – Aqaba, Jordan Malik Bataineh Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan Nabeela Abu-Alkishik Department of Mathematics, Jerash University, Jerash, Jordan Isra Al-Shbeil Department of Mathematics, Faculty of Sciences, University of Jordan, Amman 11942, Jordan Abdallah Al-Husban Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan 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 94 103 2641 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240109 https://www.americaspg.com/journal/21/article/2641 https://www.americaspg.com/storage/21712236440.pdf