To write the equation of a line in general form given the y-intercept \( b = -2 \) and gradient \( m = 5 \), we start with the slope-intercept form of the line, which is:
\[ y = mx + b \]
Substituting the given values:
\[ y = 5x - 2 \]
Next, to convert this equation into general form \( Ax + By + C = 0 \), we will rearrange the terms:
\[ 5x - y - 2 = 0 \]
To express it in the standard format \( Ax + By + C = 0 \), we can rearrange further:
\[ 5x - y = 2 \]
Thus, in general form, the equation of the line is:
\[ 5x - y - 2 = 0 \]