To find the equation of the line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can use the given slope and point.
The slope \( m \) is given as \( -\frac{1}{5} \) and the line passes through the point \( (-5, 7) \). Using this information, we can substitute these values into the point-slope form of the equation, which is:
\[ y - y_1 = m(x - x_1) \]
Substituting \( m = -\frac{1}{5} \), \( x_1 = -5 \), and \( y_1 = 7 \):
\[ y - 7 = -\frac{1}{5}(x - (-5)) \]
This simplifies to:
\[ y - 7 = -\frac{1}{5}(x + 5) \]
Now distribute \( -\frac{1}{5} \):
\[ y - 7 = -\frac{1}{5}x - 1 \]
Next, add 7 to both sides to solve for \( y \):
\[ y = -\frac{1}{5}x - 1 + 7 \]
\[ y = -\frac{1}{5}x + 6 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = -\frac{1}{5}x + 6 \]