If the eccentricity of an ellipse is $\large\frac{5}{8}$ and the distance between its foci is 10, then find latus rectum of the ellipse.

Question

$\begin{array}{1 1}\large\frac{39}{4}\\\large\frac{13}{8}\\\large\frac{26}{4}\\\large\frac{31}{8}\end{array} $