To solve the equation, we need to start from the equation given and add \(2x\) to both sides. The equation is:
\[ -2x + 5 = 4x - 7 \]
Now, let's add \(2x\) to both sides:
\[ -2x + 2x + 5 = 4x + 2x - 7 \]
This simplifies to:
\[ 5 = 6x - 7 \]
Next, we can isolate \(x\) by adding \(7\) to both sides:
\[ 5 + 7 = 6x \]
This gives:
\[ 12 = 6x \]
Now, to solve for \(x\), divide both sides by \(6\):
\[ x = \frac{12}{6} = 2 \]
Therefore, the value of \(x\) is:
\[ \boxed{2} \]