Identify the quadratic function related to a square root function.

To find the related quadratic function, we square the given square root function $k(x) = 5\sqrt{x}$. Squaring both sides, we get $(k(x))^2 = (5\sqrt{x})^2$, which simplifies to $m(x) = 25x$. However, the options provided are quadratic functions. Let's assume the question is asking for the inverse function, which is obtained by setting $y = k(x)$ and solving for $x$ in terms of $y$, then swapping $x$ and $y$. If $y = 5\sqrt{x}$, then $y^2 = 25x$, so $x = \frac{y^2}{25}$. Replacing $y$ with $x$, we get the inverse function $m(x) = \frac{x^2}{25}$.