To solve the expression [tex]\(\frac{5|x| - y^3}{x}\)[/tex] with [tex]\(x = -5\)[/tex] and [tex]\(y = 25\)[/tex], we can follow a detailed step-by-step approach:
1. Identify the Absolute Value of [tex]\(x\)[/tex]:
Since [tex]\(x = -5\)[/tex], calculate the absolute value of [tex]\(x\)[/tex]:
[tex]\[
|x| = |-5| = 5
\][/tex]
2. Calculate the Numerator:
Substitute [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the expression for the numerator [tex]\(5|x| - y^3\)[/tex]:
[tex]\[
5|x| = 5 \times 5 = 25
\][/tex]
Next, compute [tex]\(y^3\)[/tex]:
[tex]\[
y^3 = 25^3 = 25 \times 25 \times 25 = 625 \times 25 = 15625
\][/tex]
Therefore, the numerator is:
[tex]\[
5|x| - y^3 = 25 - 15625 = -15600
\][/tex]
3. Identify the Denominator:
The denominator is simply [tex]\(x\)[/tex], which is:
[tex]\[
x = -5
\][/tex]
4. Calculate the Expression:
Now, substitute the numerator and the denominator into the expression [tex]\(\frac{5|x| - y^3}{x}\)[/tex]:
[tex]\[
\frac{5|x| - y^3}{x} = \frac{-15600}{-5}
\][/tex]
Divide the numerator by the denominator:
[tex]\[
\frac{-15600}{-5} = 3120
\][/tex]
Therefore, the value of the expression [tex]\(\frac{5|x| - y^3}{x}\)[/tex] when [tex]\(x = -5\)[/tex] and [tex]\(y = 25\)[/tex] is [tex]\(3120\)[/tex].
So, the correct answer is:
[tex]\[
\boxed{3120}
\][/tex]
This matches option D. Therefore, the correct answer is D.
