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The question asks for the coordinates of \( F' \), the image of point \( F \) after reflecting across the line \( x = -1 \).

### Steps to solve:

1. **Identify the original coordinates of point \( F \):**
   \[
   F = (-5, 5)
   \]
2. **Understand the reflection rule:**
   When reflecting a point across a vertical line (in this case, \( x = -1 \)), the \( y \)-coordinate remains the same, while the \( x \)-coordinate changes based on its distance from the line of reflection.

3. **Calculate the reflection of \( F \):**
   The original point \( F \) is 4 units to the left of the line \( x = -1 \) (since \( -5 - (-1) = -4 \)).
   - The reflection point \( F' \) will be 4 units to the right of the line \( x = -1 \), giving the new \( x \)-coordinate as:
   \[
   x = -1 + 4 = 3
   \]
   The \( y \)-coordinate remains unchanged, so \( y = 5 \).

Thus, the coordinates of \( F' \) after the reflection are:
\[
F' = (3, 5)
\]

### Answer:
\( F' \) is at \( (3, 5) \), so the correct choice is:
\[
\boxed{F' (3, 5)}
\]

Would you like further clarification or details? Here are five related questions to expand the concept:

1. How would you reflect a point across a horizontal line, such as \( y = 2 \)?
2. What are the coordinates of \( U' \) after reflecting across \( x = -1 \)?
3. What is the distance between the original point \( F \) and its reflection \( F' \)?
4. How would the coordinates of point \( N \) change if reflected across \( y = 0 \)?
5. Can you describe a real-life scenario where reflections are used?

**Tip:** When reflecting a point across a vertical line, focus on adjusting only the \( x \)-coordinate while keeping the \( y \)-coordinate constant.

What are the coordinates for F' after a reflection across the line x = -1?

Learn how to reflect point F (-5, 5) across the vertical line x = -1. This problem involves using the reflection theorem to calculate the new coordinates after reflection in a coordinate plane. Suitable for students in Grades 6-8.

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