We are asked to solve the linear equation $5 + 2(x+5) = 4 - 5x$ for $x$.

1. Problem Description

We are asked to solve the linear equation $5 + 2(x+5) = 4 - 5x$ for $x$.

2. Solution Steps

First, we distribute the terms on both sides of the equation.

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

$5 + 2x + 10 = 4 - 5x$

Next, we combine like terms on the left side of the equation.

$15 + 2x = 4 - 5x$

Then, we add $5x$ to both sides of the equation.

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

$15 + 7x = 4$

Now, we subtract 15 from both sides of the equation.

$15 + 7x - 15 = 4 - 15$

$7x = -11$

Finally, we divide both sides of the equation by 7 to solve for $x$.

$\frac{7x}{7} = \frac{-11}{7}$

$x = -\frac{11}{7}$

3. Final Answer

$x = -\frac{11}{7}$