To simplify the expression \(-4z^2 + 2z^2 - 3z^2 + 5z^2\), we can combine the like terms (the terms that contain \(z^2\)).
Let's add them together:
\[ -4z^2 + 2z^2 - 3z^2 + 5z^2 \]
Now, we can group them based on their coefficients:
\[ (-4 + 2 - 3 + 5)z^2 \]
Calculating the sum of the coefficients:
\[ -4 + 2 = -2 \] \[ -2 - 3 = -5 \] \[ -5 + 5 = 0 \]
So, the simplified expression is:
\[ 0z^2 \]
This can be further simplified to just:
\[ 0 \]
So, the final result is
\[ \boxed{0} \]
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