In any decision-making process, imprecision is a significant issue. To deal with the ambiguous environment of collective decision-making, various tools and approaches have been created. Fuzzy set theory is one of the most recent approaches for coping with imprecision. The Fuzzy Transportation Problem (FTP) is a well-known network planned linear programming problem which exists in a variety of situations and has received a lot of attention recently. Many authors defined and solved the fuzzy transportation problem with frequently utilized fuzzy numbers such as triangular fuzzy numbers or trapezoidal fuzzy numbers. On the other hand, real-world problems usually involve more than four variables. To tackle these concerns, the pentagonal fuzzy number is applied to the problems. This article proposes an approach to solving transportation problems whose parameters are pentagonal fuzzy numbers without requiring an initial feasible solution. An algorithm based on the core and spread method and an extended MODI method is developed to determine the optimal solution to the problem. The proposed process is based on the approximation method and gives a more efficient result. An illustrated example is used to validate the model. As a result, the proposed methodology is both simpler and more computationally efficient than the existing approaches.