1. If the inequality $\sqrt{x}+\sqrt{y} \leqslant k \sqrt{5 x+y}$ holds for any positive real numbers $x, y$, then the minimum value of the real number $k$ is $\qquad$
By the Cauchy inequality, we have $\left(\frac{1}{5}+1\right)(5 x+y) \geqslant(\sqrt{x}+\sqrt{y})^{2} \Rightarrow \frac{\sqrt{x}+\sqrt{y}}{\sqrt{5 x+y}} \leqslant \sqrt{\frac{6}{5}}=\frac{\sqrt{30}}{5}$, equality holds when $y=25 x$. Therefore, the minimum value of the real number $k$ is $\frac{\sqrt{30}}{5}$.