The question is asking for the value of $Q(2)$, where $P(x) = -2x^3 + 3x^2 - 4x + 5$.

To solve for $Q(2)$, we substitute $x = 2$ into the polynomial equation:

$P(x) = -2x^3 + 3x^2 - 4x + 5$

Substituting $x = 2$:

$P(2) = -2(2)^3 + 3(2)^2 - 4(2) + 5$

$= -2(8) + 3(4) - 4(2) + 5$

$= -16 + 12 - 8 + 5$

$= -16 + 12 = -4$

$-4 - 8 = -12$

$-12 + 5 = -7$

So, the value of $Q(2)$ is $-7$.

Answer: $-7$.

Do you need further details or have any questions?
Here are 5 related questions to deepen your understanding:

1. How do you determine the value of a polynomial at any given point?
2. What is the degree of the polynomial $P(x) = -2x^3 + 3x^2 - 4x + 5$?
3. How does changing the sign of the coefficients affect the shape of a polynomial graph?
4. What is the difference between evaluating a polynomial and solving a polynomial equation?
5. How do you find the roots of a polynomial like $P(x)$?

Tip: When substituting values into a polynomial, be careful with negative signs and exponentiation to avoid calculation errors.