To solve the inequality \(-2x + 5 + x < 3x + 13\), we can start by simplifying the left side.
Combine like terms on the left side:
\[ -2x + x = -x \]
So the inequality now looks like:
\[ -x + 5 < 3x + 13 \]
Next, let's get all the terms involving \(x\) on one side and the constant terms on the other. We can add \(x\) to both sides:
\[ 5 < 3x + x + 13 \]
Which simplifies to:
\[ 5 < 4x + 13 \]
Next, subtract \(13\) from both sides:
\[ 5 - 13 < 4x \]
This simplifies to:
\[ -8 < 4x \]
Now, divide both sides by \(4\):
\[ -\frac{8}{4} < x \]
Which simplifies to:
\[ -2 < x \]
Or we can write it as:
\[ x > -2 \]
Thus, the solution to the inequality is:
\[ \boxed{x > -2} \]