What is the value of this expression when r = -2?

To evaluate the expression \( 2r^2 + |r + 7| - 5 \) when \( r = -2 \), we'll substitute \(-2\) for \(r\) and simplify step by step.

1. Substitute \( r = -2 \): \[ 2(-2)^2 + |-2 + 7| - 5 \]

2. Calculate \( (-2)^2 \): \[ (-2)^2 = 4 \]

3. Substitute back into the expression: \[ 2(4) + |-2 + 7| - 5 \]

4. Multiply: \[ 8 + |-2 + 7| - 5 \]

5. Simplify inside the absolute value: \[ -2 + 7 = 5 \]

6. Now the expression is: \[ 8 + |5| - 5 \]

7. Since the absolute value of 5 is 5, we have: \[ 8 + 5 - 5 \]

8. Now simplify: \[ 8 + 5 = 13 \] \[ 13 - 5 = 8 \]

Thus, the value of the expression when \( r = -2 \) is \( \boxed{8} \).