Let's solve the expression:

\[
-\frac{5}{8} + \left(-\frac{8}{5}\right)
\]

### Step 1: Address the signs
The expression involves adding two negative fractions:

\[
-\frac{5}{8} + \left(-\frac{8}{5}\right)
\]

This can be rewritten as:

\[
-\frac{5}{8} - \frac{8}{5}
\]

### Step 2: Find a common denominator
To add or subtract fractions, we need a common denominator. The denominators here are 8 and 5. The least common denominator (LCD) of 8 and 5 is 40.

### Step 3: Convert fractions to have a common denominator

1. Convert \( -\frac{5}{8} \) to a denominator of 40:
   \[
   -\frac{5}{8} = -\frac{5 \times 5}{8 \times 5} = -\frac{25}{40}
   \]

2. Convert \( -\frac{8}{5} \) to a denominator of 40:
   \[
   -\frac{8}{5} = -\frac{8 \times 8}{5 \times 8} = -\frac{64}{40}
   \]

### Step 4: Perform the subtraction
Now subtract the fractions:

\[
-\frac{25}{40} - \frac{64}{40} = -\frac{25 + 64}{40} = -\frac{89}{40}
\]

### Step 5: Simplify the fraction
The fraction \( \frac{89}{40} \) cannot be simplified further, as 89 is a prime number and does not share any common factors with 40.

So, the final result is:

\[
\boxed{-\frac{89}{40}}
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How can you convert an improper fraction like \( \frac{89}{40} \) into a mixed number?
2. What would happen if the signs were reversed in the original expression?
3. How do you add fractions with different denominators without finding the least common denominator?
4. What is the decimal equivalent of \( -\frac{89}{40} \)?
5. How would you solve the expression if both fractions were positive?

**Tip:** When dealing with fractions, finding a common denominator is key to performing addition or subtraction accurately.

Learn how to solve the expression -5/8 + (-8/5) step-by-step with a detailed solution. This problem involves fractions and negative numbers, focusing on finding a common denominator to perform subtraction. Suitable for students in Grades 6-8.

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