To simplify the expression \( 5(7x - 2) - 14x + 4 \), we start by distributing the 5:
\[ 5(7x - 2) = 5 \cdot 7x - 5 \cdot 2 = 35x - 10 \]
Now, substitute this back into the expression:
\[ 35x - 10 - 14x + 4 \]
Next, we combine like terms. First, combine the \( x \) terms:
\[ 35x - 14x = 21x \]
Now, combine the constant terms:
\[ -10 + 4 = -6 \]
Putting it all together, we get:
\[ 21x - 6 \]
Thus, the simplified expression is:
\[ \boxed{21x - 6} \]