To simplify the expression \( \frac{3}{7}x + \frac{2}{7}x \), you can combine the like terms:
\[ \frac{3}{7}x + \frac{2}{7}x = \left(\frac{3}{7} + \frac{2}{7}\right)x = \frac{5}{7}x \]
Thus, the simplified expression is \( \frac{5}{7}x \).
The correct answer is C: \( \frac{5}{7}x \).