In a direct variation, the relationship between \( y \) and \( x \) can be expressed as:
\[ y = kx \]
where \( k \) is the constant of proportionality.
Given that \( y = 35 \) when \( x = 5 \), we can substitute these values into the equation to find \( k \):
\[ 35 = k \cdot 5 \]
To solve for \( k \), divide both sides by 5:
\[ k = \frac{35}{5} = 7 \]
Therefore, the value of the constant of proportionality \( k \) is \( 7 \).