The equation of a line in slope-intercept form is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Given the slope \( m = \frac{5}{3} \) and the y-intercept \( b = -4 \), we can substitute these values into the equation:
\[ y = \frac{5}{3}x - 4 \]
This is the equation of the line with a slope of \( \frac{5}{3} \) and a y-intercept of -4.