The problem involves solving the equation:

\[
|5 - 8m| = 13
\]

To solve this, we will split the absolute value equation into two separate cases:

### Case 1: 
\[
5 - 8m = 13
\]

### Case 2: 
\[
5 - 8m = -13
\]

#### Solving Case 1:

1. \( 5 - 8m = 13 \)
2. Subtract 5 from both sides:
   \[
   -8m = 13 - 5
   \]
   \[
   -8m = 8
   \]
3. Divide both sides by -8:
   \[
   m = \frac{8}{-8} = -1
   \]

#### Solving Case 2:

1. \( 5 - 8m = -13 \)
2. Subtract 5 from both sides:
   \[
   -8m = -13 - 5
   \]
   \[
   -8m = -18
   \]
3. Divide both sides by -8:
   \[
   m = \frac{-18}{-8} = \frac{9}{4}
   \]

### Solution:
The two possible values for \( m \) are:
\[
m = -1 \quad \text{or} \quad m = \frac{9}{4}
\]

Would you like more details on any step? 

Here are 5 related questions for practice:

1. Solve \( |3 - 7x| = 10 \).
2. Find the solution to \( |2x + 1| = 5 \).
3. What are the solutions to \( |9x - 4| = 20 \)?
4. Solve \( |x + 6| = 12 \).
5. If \( |4 - 5y| = 8 \), what is \( y \)?

**Tip:** Always remember that absolute value equations can result in two different cases to account for both positive and negative solutions.

Learn how to solve the absolute value equation |5 - 8m| = 13 using step-by-step instructions. This solution includes splitting the equation into two cases and solving for 'm'. Suitable for students in Grades 8-10.

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