Determine the set of parametric equations for the hyperbola with vertices at $(5, 0)$ and $(-5, 0)$, and foci at $(8, 0)$ and $(-8, 0)$.

$x=5\sec(t),y=\sqrt{39}\tan(t)$

$x=\sqrt{39}\sec(t),y=5\tan(t)$

$x = 8\sec(t), y = 5\tan(t)$

$x=5\tan(t),y=\sqrt{39}\sec(t)$