2. If the quadratic function $y=x^{2}+(k+2) x+k+5$ intersects the $x$-axis at two different points with both coordinates being positive, then the value of $k$ should be ( ).
(A) $k>4$ or $k<-5$
(B) $-5<k<-4$
(C) $k \geqslant-4$ or $k \leqslant-5$
(D) $-5 \leqslant k \leqslant-4$
2. (B).

According to the problem, we have
$$
\left\{\begin{array}{l}
k+5>0, \\
(k+2)^{2}-4(k+5)>0 .
\end{array}\right.
$$

Solving this, we get $-5<k<-4$.