A finite group G is called a DCI-group if two Cayley digraphs over G are isomorphic if and only if their connection sets are conjugate by a group automorphism. We prove that the group C-2(5) x C-p, where p is a prime, is a DCI-group if and only if p not equal 2. Together with the previously obtained results, this implies that a group G of order 32p, where p is a prime, is a DCI-group if and only if p not equal 2 and G similar or equal to C-2(5) x C-p.