Chapter 1, Equations and Inequalities - 1.7 Solve Absolute Value Equations and Inequalities - 1.7 Exercises - Skill Practice - Page 55: 16

$$m=-6\quad \mathrm{or}\quad \:m=-4$$

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: $$m+5=-1\quad \mathrm{or}\quad \:m+5=1 \\ m=-6\quad \mathrm{or}\quad \:m=-4$$