UKMT Senior Mathematical Challenge, 2017

The arithmetic mean, $A$, of any two positive numbers $x$ and $y$ is defined to be $A = \frac{1}{2}(x+y)$ and their geometric mean, $G$, is defined to be $G = \sqrt{xy}$. For two particular values $x$ and $y$, with $x > y$, the ratio $A:G = 5:4$. For these values of $x$ and $y$, what is the ratio $x:y$?

(A) $5:4$ (B) $2:1$ (C) $5:2$ (D) $7:2$ (E) $4:1$