It looks like there was a minor mistake in how the equation was written. It should probably be: 

\[
5(x + 2) = 5x - 10
\]

I'll solve this equation for you.

### Step-by-Step Solution:

1. **Distribute the 5 on the left side:**

\[
5 \cdot x + 5 \cdot 2 = 5x - 10
\]

This simplifies to:

\[
5x + 10 = 5x - 10
\]

2. **Subtract \(5x\) from both sides:**

\[
5x + 10 - 5x = 5x - 10 - 5x
\]

This simplifies to:

\[
10 = -10
\]

### Conclusion:

The result \(10 = -10\) is a contradiction, which means there is **no solution** to this equation. In other words, the equation is inconsistent and cannot be true for any value of \(x\).

Would you like more details on this solution or have any questions? Here are some related questions that you might find helpful:

1. How do you identify if an equation has no solution?
2. What is the difference between no solution, infinite solutions, and a unique solution in equations?
3. How can we solve equations with variables on both sides?
4. What are some common mistakes to avoid when solving linear equations?
5. How do you solve and graph inequalities?

**Tip:** When solving equations, always check for contradictions or identities to determine the type of solution (no solution, infinite solutions, or a unique solution).

This webpage provides a detailed step-by-step solution to the linear equation 5(x + 2) = 5x - 10. The problem explores algebraic techniques, including the distributive property and simplification of linear equations, leading to the conclusion that there is no solution. Suitable for Grades 6-8 students studying algebra.

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