5. Let $a, b, c$ be three numbers chosen from $1,2, \cdots, 5$ (no repetition allowed), and $ab+c$ is an odd number. Then the number of all possible values is ( ).
(A)6
(B) 7
(C) 8
(D) 9
5. D.

The 9 possible values that meet the requirements are
$$
5,7,9, 11,13, 17,19, 21,23
$$