Let's break down the expression step by step:

\[ 2^{3.15} - [115 - (12 - 5)^2] \]

1. **Calculate the exponentiation:**
\[ 2^{3.15} \]
Using a calculator, we find:
\[ 2^{3.15} \approx 8.815 \]

2. **Calculate the inner parentheses:**
\[ 12 - 5 = 7 \]

3. **Square the result:**
\[ 7^2 = 49 \]

4. **Subtract from 115:**
\[ 115 - 49 = 66 \]

5. **Combine the results:**
\[ 2^{3.15} - 66 \approx 8.815 - 66 = -57.185 \]

So, the final result is approximately:
\[ -57.185 \]