The pentagonal neutrosophic number is an extended version of single typed neutrosophic number. Real-humankind problems have different sorts of ambiguity in nature and amongst them; one of the important problems is solving the networking problem. In this contribution, the conception of pentagonal neutrosophic numbers 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 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.