To find the slope of line \( e \) that is perpendicular to line \( d \) with a slope of \( \frac{3}{5} \), we need to use the property that the product of the slopes of two perpendicular lines is \(-1\).
Let \( m_d = \frac{3}{5} \) (the slope of line \( d \)) and \( m_e \) be the slope of line \( e \). The relationship can be expressed as:
\[ m_e \cdot m_d = -1 \]
Substituting the value of \( m_d \):
\[ m_e \cdot \frac{3}{5} = -1 \]
Now, solve for \( m_e \):
\[ m_e = -1 \cdot \frac{5}{3} = -\frac{5}{3} \]
Thus, the slope of line \( e \) is
\[ \boxed{-\frac{5}{3}} \]