We need to solve the equation $4x - 2(x+1) = 5(x+3) + 5$ for $x$.

1. Problem Description

We need to solve the equation $4x - 2(x+1) = 5(x+3) + 5$ for $x$.

2. Solution Steps

First, we expand both sides of the equation:

$4x - 2(x+1) = 5(x+3) + 5$

$4x - 2x - 2 = 5x + 15 + 5$

$2x - 2 = 5x + 20$

Next, we subtract $2x$ from both sides:

$2x - 2 - 2x = 5x + 20 - 2x$

$-2 = 3x + 20$

Now, we subtract $20$ from both sides:

$-2 - 20 = 3x + 20 - 20$

$-22 = 3x$

Finally, we divide both sides by $3$ to isolate $x$:

$\frac{-22}{3} = \frac{3x}{3}$

$x = -\frac{22}{3}$

3. Final Answer

$x = -\frac{22}{3}$