2. Let positive integers $x \neq y$, and satisfy $-\frac{1}{x}+\frac{1}{y}=\frac{2}{5}$. Then the units digit of $x^{y}+$ $y^{x}$ is ( ).
(A) 2
(B) 3
(C) 5
(D) 7
2. (A).

From $\frac{1}{x}+\frac{1}{y}=\frac{2}{5}$ we get $2 x y-5 x-5 y=0$. Then $4 x y-10 x-10 y+25=25$,
which simplifies to $(2 x-5)(2 y-5)=25$.
Since $x, y$ are positive integers, and $x \neq y$,
$$
\therefore\left\{\begin{array}{l}
2 x-5=1,5,25, \\
2 y-5=25,5,1 .
\end{array}\right.
$$

Solving, we get $\left\{\begin{array}{l}x=3,15,5, \\ y=15,3,5 .\end{array}\left(\right.\right.$ where $\left\{\begin{array}{l}x=5 \\ y=5\end{array}\right.$, is discarded $)$ Also, since the unit digit of $3^{15}$ is $7$, and the unit digit of $15^{3}$ is $5$, $\therefore$ the unit digit of $x^{y}+y^{x}$ is $2$.