1. Given the sets $A=\left\{2,4, a^{3}-2 a^{2}-a+7\right\}, B=\left\{-4, a+3, a^{2}-2 a+2, a^{3}+a^{2}+3 a+7\right\}$ $(a \in \mathbf{R})$. If $A \cap B=\{2,5\}$, then the real number $a=$ $\qquad$ .
1. 2 .

From $5 \in A$ we know $a^{3}-2 a^{2}-a+7=5$, thus we get $(a+1)(a-1)(a-2)=0$, hence $a \in\{-1,1,2\}$. If $a=-1$, then $B=\{-4,2,5,4\}$, at this time $A=\{2,4,5\}, A \cap B=\{2,4,5\}$, which does not meet the condition; If $a=1$, then $B=\{-4,4,1,12\}$, by $5 \notin B$ we know $a=1$ does not meet the condition; If $a=2$, then $B=\{-4,5,2,25\}$, at this time $A=\{2,4,5\}, A \cap B=\{2,5\}$, which meets the condition.
Therefore, the real number $a=2$.