To find the x-intercept of the line given by the equation \( 5x + 17y = -25 \), we set \( y = 0 \) and solve for \( x \).
Starting with the equation:
\[ 5x + 17(0) = -25 \]
This simplifies to:
\[ 5x = -25 \]
Now, divide both sides by 5:
\[ x = -5 \]
Thus, the x-intercept of the line is at the point \((-5, 0)\).