5. Let $A=\{0,1,2,3\}, B=\{2,3,4,5,6\}$, and the mapping $f: A \rightarrow B$ satisfies that for any $x \in A, x + f(x) + x f^{2}(x)$ is an odd number. Then the number of such mappings is ( ).
(A) 80
(B) 100
(C) 250
(D) 625
5. B.

Notice that when $x=0,2$, $f(x)$ can take the values 3,5; when $x=1,3$, $f(x)$ can take any value in $B$. Therefore, the number of $f(x)$ is $2 \times 2 \times 5 \times 5=100$.