The problem is to solve the fractional equation $\frac{2x+2}{x-2} = 5$.

1. Problem Description

The problem is to solve the fractional equation $\frac{2x+2}{x-2} = 5$.

2. Solution Steps

To solve the equation $\frac{2x+2}{x-2} = 5$, we first multiply both sides by $(x-2)$ to eliminate the fraction.

$2x + 2 = 5(x-2)$

Expand the right side:

$2x + 2 = 5x - 10$

Subtract $2x$ from both sides:

$2 = 3x - 10$

Add $10$ to both sides:

$12 = 3x$

Divide both sides by $3$:

$x = \frac{12}{3}$

$x = 4$

Now we check the solution by substituting $x=4$ into the original equation:

$\frac{2(4)+2}{4-2} = \frac{8+2}{2} = \frac{10}{2} = 5$

Since the left side equals the right side, $x=4$ is the solution.

3. Final Answer

The final answer is $x=4$.