Let $E$ be an ellipse whose axes are parallel to the co-ordinates axes, having its center at $(3,-4)$, one focus at $(4,-4)$ and one vertex at $(5,-4)$. If $m x-y=4, m>0$ is a tangent to the ellipse $E$, then the value of $5 m^2$ is equal to $\_\_\_\_$ .
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