To solve the equation \( 4(-2x + 5) + 5x + 4 = 27 \), we can start by distributing the \( 4 \) in the first term:
\[ 4(-2x) + 4(5) + 5x + 4 = 27 \]
This simplifies to:
\[ -8x + 20 + 5x + 4 = 27 \]
Next, we combine like terms on the left side:
\[ (-8x + 5x) + (20 + 4) = 27 \]
This gives us:
\[ -3x + 24 = 27 \]
Now, we can isolate \( x \) by first subtracting \( 24 \) from both sides:
\[ -3x = 27 - 24 \]
This simplifies to:
\[ -3x = 3 \]
Next, divide both sides by \( -3 \):
\[ x = \frac{3}{-3} \]
This gives us:
\[ x = -1 \]
Thus, the solution to the equation \( 4(-2x + 5) + 5x + 4 = 27 \) is:
\[ \boxed{-1} \]