To find the equation of a line that is parallel to the line \(y = 25x + 1\) and passes through the point \((5, 5)\), we need to use the fact that parallel lines have the same slope.
The slope of the given line \(y = 25x + 1\) is \(25\). Therefore, the line we are looking for will also have a slope of \(25\).
Using the point-slope form of a linear equation, which is given by:
\[ y - y_1 = m(x - x_1) \]
where \(m\) is the slope and \((x_1, y_1)\) is the point through which the line passes, we can substitute \(m = 25\), \(x_1 = 5\), and \(y_1 = 5\):
\[ y - 5 = 25(x - 5) \]
Now, we can simplify this equation:
\[ y - 5 = 25x - 125 \]
Adding \(5\) to both sides gives:
\[ y = 25x - 120 \]
Thus, the equation of the line that is parallel to \(y = 25x + 1\) and passes through the point \((5, 5)\) is:
\[ \boxed{y = 25x - 120} \]