14 ){\begin{aligned}(\sqrt{5})^{2x+y} &= \sqrt{\frac{1}{5}}\cdot \sqrt{5}\\(\frac{1}{5})^{x}\cdot 5^{y} &= 125\end{aligned}}

$$\begin{aligned}&\begin{cases}(\sqrt{5})^{2x+y} = \sqrt{\frac{1}{5}}\cdot \sqrt{5}\\(\frac{1}{5})^{x}\cdot 5^{y} = 125\end{cases}\\&\begin{cases}(5^{\frac{1}{2}})^{2x+y} = (5^{-\frac{1}{2}})^{\frac{1}{2}}\cdot 5^{\frac{1}{2}}\\5^{-x}\cdot 5^{y} = 5^{3}\end{cases}\\&\begin{cases}5^{\frac{1}{2}(2x+y)} = 5^{-\frac{1}{4}} \cdot 5^{\frac{1}{2}}\\5^{-x+y} = 5^{3}\end{cases}\\&\begin{cases}\frac{1}{2}(2x+y) = -\frac{1}{4} + \frac{1}{2}\\-x+y = 3\end{cases}\\&\begin{cases}2x+y = \frac{1}{2}\\-x+y = 3\end{cases}\end{aligned}$$ Выразим из второго уравнения y: $$y = 3 + x$$ Подставим в первое уравнение: $$\begin{aligned}&2x + 3 + x = \frac{1}{2}\\&3x = \frac{1}{2} - 3\\&3x = -\frac{5}{2}\\ &x = -\frac{5}{6}\end{aligned}$$ $$y = 3 - \frac{5}{6} = \frac{18}{6} - \frac{5}{6} = \frac{13}{6}$$ Ответ: x=-5/6; y=13/6