Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: Let \[f(x) = \left\{
\begin{array}{cl}
2x + 7 & \text{if } x < -2, \\
-x^2 - x + 1 & \text{if } x \ge -2.
\end{array}
\right.\]Find the sum of all values of $x$ such that $f(x) = -5.$
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