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.