Find the equation for the ellipse that satisfies the given conditions: Length of major

Length of major axis $=26 ;$ foci $=(\pm 5,0)$.

Since the foci are on the x-axis, the major axis is along the x-axis.

Therefore, the equation of the ellipse will be of the form $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$, where $a$ is the semi-major axis.

Accordingly, 2a = 26 ⇒ a = 13 and c = 5.

It is known that $a^{2}=b^{2}+c^{2}$.

$\therefore 13^{2}=b^{2}+5^{2}$

$\Rightarrow 169=b^{2}+25$

$\Rightarrow b^{2}=169-25$

$\Rightarrow b=\sqrt{144}=12$

Thus, the equation of the ellipse is $\frac{x^{2}}{13^{2}}+\frac{y^{2}}{12^{2}}=1$ or $\frac{x^{2}}{169}+\frac{y^{2}}{144}=1$.