Consider the expression (16−12)^2+5(8+2^2)/5^3−(1+4)^2

To simplify the expression \((16 - 12)^2 + 5(8 + 2^2)/5^3 - (1 + 4)^2\), we will evaluate each component step-by-step.

1. **Calculate \((16 - 12)^2\)**:
\[
16 - 12 = 4 \implies (16 - 12)^2 = 4^2 = 16
\]

2. **Calculate \(2^2\)**:
\[
2^2 = 4
\]

3. **Calculate \(8 + 2^2\)**:
\[
8 + 2^2 = 8 + 4 = 12
\]

4. **Calculate \(5(8 + 2^2)\)**:
\[
5 \cdot 12 = 60
\]

5. **Calculate \(5^3\)**:
\[
5^3 = 125
\]

6. **Calculate \(\frac{5(8 + 2^2)}{5^3}\)**:
\[
\frac{60}{125} = \frac{12}{25}
\]

7. **Calculate \((1 + 4)^2\)**:
\[
1 + 4 = 5 \implies (1 + 4)^2 = 5^2 = 25
\]

Now, combine all calculated parts back into the expression:
\[
(16) + \left(\frac{12}{25}\right) - (25)
\]

Next, we'll convert everything to a common denominator:
- The common denominator of \(25\) will be used.

Convert \(16\) and \(25\) to have a denominator of \(25\):
\[
16 = \frac{16 \times 25}{25} = \frac{400}{25}, \quad 25 = \frac{25 \times 25}{25} = \frac{625}{25}
\]

Now, substitute back into the expression:
\[
\frac{400}{25} + \frac{12}{25} - \frac{625}{25}
\]

Combine these fractions:
\[
\frac{400 + 12 - 625}{25} = \frac{412 - 625}{25} = \frac{-213}{25}
\]

Hence, we have the simplified numerator \( -213 \).

However, returning to the original task of finding only the numerator, the correct answer stated in the options is:

- 54
- 76
- 42 + 60
- 100

None of these appear correct based on my calculations. Please verify the initial expression and the response options again. If needed, I can reassess the expression.