K-means clustering is one of the most popular clustering algorithms, which defines k number of clusters by minimizing the distances between cluster centers and the data points. If the data points include any level of human judgements, they tend to be vague and imprecise due to the difficulty of providing accurate evaluations. After the ordinary fuzzy sets' introduction to the literature, it has been successfully applied to such cases and various extensions are proposed. One of the recent extensions is q-rung orthopair fuzzy sets where the sum of the qth power of the membership degree and the qth power of the non-membership degree is bounded by one thus the space of acceptable orthopairs increases and provides more freedom for decision makers to express their judgements. In this study, a new penthagorean fuzzy k-means clustering method is developed. The 5th power is used as a special case of q-rung orthopair fuzzy sets and named as penthagorean fuzzy sets. The proposed approach is illustrated with an example of The Motion Picture Association of America film rating system.