This paper proposes a novel extension of the classical transportation problem, called the Neutrosophic Pentagonal Solid Interval Transportation Problem (NPSITP). It models uncertainties in supply, demand, and transport parameters using pentagonal neutrosophic numbers, while transportation costs are represented as intervals. The interval-valued cost objective is decomposed into two deterministic objectives based on its expected value and associated uncertainty measure. Constraints are converted into crisp form using a score function for better interpretability. A fuzzy programming method is then applied to find a Pareto optimal solution, and a real-life example solved using LINGO 20.0 demonstrates the approach.