The problem states that $F(x+2) = 2x^2 + 7x - 5$. We need to find the value of $F(-1)$.

1. Problem Description

The problem states that $F(x+2) = 2x^2 + 7x - 5$. We need to find the value of $F(-1)$.

2. Solution Steps

First, we need to find the value of $x$ for which $x+2 = -1$.

$x+2 = -1$

$x = -1 - 2$

$x = -3$

Now that we have $x = -3$, we can substitute this value into the expression for $F(x+2)$ to find $F(-1)$.

$F(-1) = F((-3)+2) = 2(-3)^2 + 7(-3) - 5$

$F(-1) = 2(9) - 21 - 5$

$F(-1) = 18 - 21 - 5$

$F(-1) = -3 - 5$

$F(-1) = -8$

3. Final Answer

The final answer is -8.