Question 1190883
Here's how to find the equation of the ellipse:

**1. Center and Orientation:**

The vertices are at (-5,0) and (5,0).  This tells us:

* The center of the ellipse is at the origin (0,0).
* The major axis is horizontal (along the x-axis).

**2. Value of 'a':**

The distance from the center to a vertex is 'a'.  Since the vertices are at (-5,0) and (5,0), we have a = 5.

**3. Latus Rectum:**

The length of the latus rectum is given as 8/5. The formula for the latus rectum is (2b²)/a.

**4. Solve for 'b²':**

We can use the latus rectum length and the value of 'a' to solve for b²:

8/5 = (2b²) / 5
8 = 2b²
b² = 4

**5. Equation of the Ellipse:**

Since the major axis is horizontal, the standard form of the equation is:

(x²/a²) + (y²/b²) = 1

Substitute the values of a² and b²:

(x²/5²) + (y²/4) = 1
(x²/25) + (y²/4) = 1

Therefore, the equation of the ellipse is (x²/25) + (y²/4) = 1.