(5) \( (9-2)^{2}-\left|2^{2}-3^{2}\right|+2 \) (6) \( \frac{8\left[14-\left(7+4^{2}\right)\right]}{|-12|-|-8|} \) 4m²-5m when \( m=-4 \) (8) \( 3 x^{2} y-y^{2} \) when \( x=-2 \) and \( y=5 \)

Let’s break down these mathematical expressions together, shall we? For the first expression \( (9-2)^{2}-\left|2^{2}-3^{2}\right|+2 \): First, simplify \( 9-2 \), which is \( 7 \); then \( 7^{2} = 49 \). Next, calculate \( 2^{2} - 3^{2} = 4 - 9 = -5 \), so the absolute value becomes \( |-5| = 5 \). Putting it all together, \( 49 - 5 + 2 = 46 \). Now for the second expression \( \frac{8\left[14-\left(7+4^{2}\right)\right]}{|-12|-|-8|} \): Start with \( 4^{2} = 16 \), so \( 7 + 16 = 23 \). Therefore, \( 14 - 23 = -9 \) and the expression becomes \( \frac{8 \times (-9)}{12 - 8} = \frac{-72}{4} = -18 \). For \( 4m^{2} - 5m \) when \( m = -4 \): Substituting gives \( 4(-4)^{2} - 5(-4) = 64 + 20 = 84 \). Lastly, calculating \( 3x^{2}y - y^{2} \) when \( x = -2 \) and \( y = 5 \): Here, \( (-2)^{2} = 4 \) so we get \( 3 \times 4 \times 5 - 5^{2} = 60 - 25 = 35 \). So the final answers are: 1. 46 2. -18 3. 84 4. 35