To solve the expression \((16 - 12)^2 + 5(8 + 22) \cdot 53 - (1 + 4)^2\), we will break it down step by step.
1. **Calculate \((16 - 12)^2\)**:
\[
16 - 12 = 4 \quad \Rightarrow \quad (4)^2 = 16
\]
2. **Calculate \(8 + 22\)**:
\[
8 + 22 = 30
\]
3. **Now calculate \(5 \cdot (8 + 22) \cdot 53\)** (which is \(5 \cdot 30 \cdot 53\)):
\[
5 \cdot 30 = 150
\]
Now multiply by \(53\):
\[
150 \cdot 53 = 7950
\]
4. **Calculate \((1 + 4)^2\)**:
\[
1 + 4 = 5 \quad \Rightarrow \quad (5)^2 = 25
\]
5. **Now, combine all parts**:
\[
\text{Numerator} = 16 + 7950 - 25
\]
Calculate \(16 - 25\):
\[
16 - 25 = -9
\]
Now add \(7950\):
\[
-9 + 7950 = 7941
\]
So, the simplified numerator is \(7941\).
None of the provided options (76, 42 + 60, 4 squared plus 60, 100, 54) appear to match this result. The correct simplified numerator we calculated is **7941**.