1. Let the set $\left\{\left.\frac{5}{x}+y \right\rvert\, 1 \leqslant x \leqslant y \leqslant 5\right\}$ have its maximum and minimum elements as $M, N$, respectively, then $M N=$
Since $\frac{5}{x}+y \geqslant \frac{5}{x}+x \geqslant 2 \sqrt{5}$, equality holds when $x=y=\sqrt{5}$, then $N=2 \sqrt{5}$; also $\frac{5}{x}+y \leqslant 10$, equality holds when $x=1, y=5$, then $M=10$. Therefore, $M N=20 \sqrt{5}$.