Given parabola $y^2=5 x$
Let $\left(x_1, y_1\right)$ and $\left(x_2, y_2\right)$ be the end points of a focal chord.
So, $x_1=\frac{5}{4} t_1^2$ and $y_1=\frac{5}{4} t_1$
Since, $t_1 t_2=-1$ as $t_1$ and $t_2$ are the end points of a focal chord
$\therefore \quad x_2=\frac{5}{4}\left(\frac{1}{t_1^2}\right) \text { and } y_2=\frac{5}{2}\left(\frac{-1}{t_1}\right)$
Now, $x_1 x_2=\frac{25}{16}$
and $y_1 y_2=-\frac{25}{4}$
$\begin{aligned}
& \therefore \quad 4 x_1 x_2+y_1 y_2=4\left(\frac{25}{16}\right)-\frac{25}{4} \\
& \frac{25}{4}-\frac{25}{4}=0
\end{aligned}$