Chapter 1, Equations and Inequalities - 1.7 Solve Absolute Value Equations and Inequalities - 1.7 Exercises - Skill Practice - Page 55: 19

$$q=-2\quad \mathrm{or}\quad \:q=12$$

Since the value inside the absolute value can be positive or negative and get the same number, we must consider both options. Doing this, we find: $$\left|5-q\right|=7 \\ 5-q=-7\quad \mathrm{or}\quad \:5-q=7 \\ q=-2\quad \mathrm{or}\quad \:q=12$$