Find the equation of an ellipse satisfying the given conditions.
Foci: $(-5,0)$ and $(5,0)$, length of major axis: 14

The equation of the ellipse is $◻$,
(Simplify your answer. Use integers or fractions for any numbers in the expression.)

Step 1 ：Given the foci at $(-5,0)$ and $(5,0)$, and the length of the major axis is 14.

Step 2 ：The semi-major axis $a$ is half the length of the major axis, so $a=\frac{14}{2}=7$.

Step 3 ：The distance from the center to each focus $c$ is 5.

Step 4 ：Using the relationship $c^2=a^2-b^2$, we can find $b^2$.

Step 5 ：Substitute the known values to find $b^2$: $5^2=7^2-b^2$ which simplifies to $b^2=49-25=24$.

Step 6 ：The semi-minor axis $b$ is the square root of $b^2$, so $b=\sqrt{24}\approx 4.898979485566356$.

Step 7 ：The equation of the ellipse is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$.

Step 8 ：Substitute the values of $a$ and $b$ into the equation: $\frac{x^2}{7^2}+\frac{y^2}{24}=1$.

Step 9 ：Simplify the equation to get the final answer: $\boxed{{\displaystyle \frac{x^2}{49}+\frac{y^2}{24}=1}}$.