Answer
$\displaystyle \frac{x^{2}}{64}+\frac{y^{2}}{39}=1$
Work Step by Step
With the given information,
foci are $c=$5 units right and 5 units left of (0,0)
the major axis is horizontal, $a=8$
so the standard form the equation is
$\displaystyle \frac{(x-h)^{2}}{a^{2}}+ \displaystyle \frac{(y-k)^{2}}{b^{2}}=1$
$(h,k)=(0,0)$
$a=8$
$c=5$
From $b^{2}=a^{2}-c^{2}$
$b^{2}=64-25=39$
so the equation is
$\displaystyle \frac{x^{2}}{64}+\frac{y^{2}}{39}=1$
