The expression you've provided is: 

\[
- \frac{5}{4} \div \frac{13}{8} - \left(-\frac{8}{5}\right)
\]

To solve this, we’ll follow the order of operations (PEMDAS/BODMAS):

### Step 1: Division of Fractions
\[
- \frac{5}{4} \div \frac{13}{8}
\]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
- \frac{5}{4} \times \frac{8}{13} = - \frac{40}{52} = - \frac{10}{13}
\]

### Step 2: Simplify the Negative Sign
The expression now becomes:
\[
- \frac{10}{13} - \left(-\frac{8}{5}\right)
\]
Since subtracting a negative is the same as adding:
\[
- \frac{10}{13} + \frac{8}{5}
\]

### Step 3: Find a Common Denominator
The least common multiple of 13 and 5 is 65. Converting each fraction:
\[
- \frac{10}{13} = - \frac{50}{65}
\]
\[
\frac{8}{5} = \frac{104}{65}
\]

### Step 4: Combine the Fractions
\[
- \frac{50}{65} + \frac{104}{65} = \frac{54}{65}
\]

### Final Answer
\[
\frac{54}{65}
\]

Would you like more details on any steps? Here are some related questions to explore further:

1. What are the rules for dividing fractions?
2. How do you simplify complex fractions?
3. What is the process for finding a common denominator?
4. How does changing signs affect addition and subtraction in fractions?
5. How can you check answers in fraction problems?

**Tip:** When dividing by a fraction, remember you can multiply by its reciprocal for easier calculations.

Explore the solution to the expression −5/4 ÷ 13/8 − (−8/5) with a step-by-step breakdown. This guide covers fraction operations, including division and addition with negative fractions, and finding a common denominator. Ideal for students in Grades 6-8.

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