2. A. Given the system of inequalities about $x$
$$
\left\{\begin{array}{l}
\frac{2 x+5}{3}-x>-5, \\
\frac{x+3}{2}-t<x
\end{array}\right.
$$

has exactly five integer solutions. Then the range of $t$ is ( ).
(A) $-6<t<-\frac{11}{2}$
(B) $-6 \leqslant t<-\frac{11}{2}$
(C) $-6<t \leqslant-\frac{11}{2}$
(D) $-6 \leqslant t \leqslant-\frac{11}{2}$
2. A. C.

From the system of inequalities, we get
$$
3-2 t<x<20 \text {. }
$$

Since the system of inequalities has exactly five integer solutions, the integer solutions can only be $15, 16, 17, 18, 19$.
Thus, $14 \leqslant 3-2 t<15 \Rightarrow-6<t \leqslant-\frac{11}{2}$.