Senior Mathematical Challenge 2017 Q18

The arithmetic mean, $A$, of any two positive numbers $x$ and $y$ is defined to be $A=\frac{1}{2}\left(x+y\right)$ 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 $x:y$?