To solve this problem, let's break it down into steps:

Step 1: Find the determinant of matrix A
The determinant of a square matrix is a scalar value that represents certain properties of the matrix. In this case, we need to find the determinant of matrix A.

Step 2: Multiply the determinant by 5
Once we have the determinant of matrix A, we need to multiply it by 5 to find | 5A |.

Step 3: Simplify the expression
Finally, we simplify the expression to determine the correct answer.

Let's go through each step in detail:

Step 1: Find the determinant of matrix A
The determinant of a 3x3 matrix can be calculated using the formula:

| A | = a(ei - fh) - b(di - fg) + c(dh - eg)

where a, b, c, d, e, f, g, h, and i represent the elements of matrix A.

Step 2: Multiply the determinant by 5
Now that we have the determinant of matrix A, we multiply it by 5:

| 5A | = 5 * | A |

Step 3: Simplify the expression
To simplify the expression, we need to evaluate the determinant of matrix A and then multiply it by 5.

Since we don't have the specific values of matrix A, we can't calculate the determinant. However, we can still determine the relationship between | 5A | and | A |.

When we multiply a matrix by a scalar, such as 5, the determinant is also multiplied by the same scalar. This property is known as the scalar multiple property of determinants.

Therefore, the correct answer is option C: 125 | A |.