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

To simplify the numerator of the expression \((16−12)^2+5(8+2^2)\), we can break it down step-by-step:

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

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

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

4. **Now calculate \(5(8 + 2^2)\):**
\[
5 \times 12 = 60
\]

5. **Add the results for the numerator:**
\[
(16) + (60) = 76
\]

Thus, the simplified numerator is \(76\). Therefore, the response is:

**76**