Thin Monodromy in O(5)

R\'esum\'e This article studies the orthogonal hypergeometric groups of degree five. We establish the thinness of 12 out of the 19 hypergeometric groups of type O (3, 2) from [ 4 , Table 6]. Some of these examples are associated with Calabi-Yau 4-folds. We also establish the thinness of 9 out of the 17 hypergeometric groups of type O (4, 1) from [ 13 ], where the thinness of 7 other cases was already proven. The O (4, 1) type groups were predicted to be all thin and our result leaves just one case open.