Real-human kind issues have distinct sort of ambiguity and among them; one of the critical troubles is solving the shortest path problem. In this contribution, we applied the developed score function and accuracy function of pentagonal neutrosophic number (PNN) into a shortage path selection problem. Further, a time dependent and heuristic cost function related shortest path algorithm is considered here in PNN area and solved it utilizing an influx of dissimilar rational & pioneer thinking. Lastly, estimation of total ideal time of the graph reflects the importance of this noble work.