Let\[f(x) = \left\{ \begin{array}{cl} 2x + 7 & \text{if } x < -2, \\ -x^2 - x + 1 & \text{if } x \ge -2. \end{array} \right.\]

2x + 7 = -5

x = -6

 

-x^2 - x + 1 = -5

-x^2 - x + 6 = 0

x = -3, x = 2

 

Sum of solution is (-6) + (-3) + 2 = -7.