International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS 2020 2020 A New Score Function of Pentagonal Neutrosophic Number and its Application in Networking Problem Department of Basic Science, Narula Institute of Technology, Agarpara, Kolkata-700109, India and Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India Avishek Chakraborty Pentagonal neutrosophic number is an extended version of a single typed neutrosophic number. Real-humankind problems have different sorts of ambiguity in nature and among them; one of the important problems is solving the networking problem. In this contribution, the conception of pentagonal neutrosophic number has been focused on a distinct framework of reference. Here, we develop a new score function and its estimation has been formulated from different perspectives. Further, a time computing-based networking problem is considered herein the pentagonal neutrosophic arena and solved it using an influx of dissimilar logical & innovative thinking. Lastly, the computation of the total completion time of the problem reflects the impotency of this noble work. 2020 2020 40 51 10.54216/IJNS.010102