Let ${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$ (a > b) be a given ellipse, length of whose latus rectum is 10. If its eccentricity is the maximum value of the function,
$\phi \left( t \right) = {5 \over {12}} + t - {t^2}$, then a² + b² is equal to :