  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 [12], 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.
