5. If $m$ and $n$ are odd numbers, the quadratic equation $x^{2}+$ $m x+n=0$ has two real roots, then the nature of these real roots is ( ).
(A) There are both odd and even roots
(B) There are neither odd nor even roots
(C) There are even roots, but no odd roots
(D) There are odd roots, but no even roots
5.B.

If $x^{2}+m x+n=0 (m, n$ are odd numbers) has integer roots, then both roots are integers and are odd (since $n$ is odd). Therefore, their sum is even, which contradicts the fact that $m$ is odd.