Since \( y \) varies directly with \( x \), we can express this relationship as:
\[ y = kx \]
where \( k \) is the constant of proportionality. We are given that \( y = 35 \) when \( x = 5 \).
Substituting the given values into the equation:
\[ 35 = k \cdot 5 \]
To find \( k \), we can solve for it:
\[ k = \frac{35}{5} = 7 \]
Thus, the constant of proportionality \( k \) is:
\[ \boxed{7} \]