To find the intersection point \( P \) of the lines \( y = 5x - 3 \) and \( y = 2x + 9 \), we need to solve these two equations simultaneously.

Step-by-Step Solution:

1. Set the equations equal to each other:

Since both equations are equal to \( y \), set them equal to each other:
\[
5x - 3 = 2x + 9
\]

2. Solve for \( x \):

\[
5x - 2x = 9 + 3
\]
\[
3x = 12
\]
\[
x = \frac{12}{3} = 4
\]

3. Substitute \( x = 4 \) back into either equation to find \( y \). Using \( y = 5x - 3 \):

\[
y = 5(4) - 3
\]
\[
y = 20 - 3
\]
\[
y = 17
\]


The coordinates of the intersection point \( P \) are \( (4, 17) \).

The correct answer is C. (4, 17)