Step 1: Sensitivity of Ammeter.
The sensitivity of a meter is inversely proportional to the range. The original meter has a range of 50 mA, and after conversion, the range becomes 500 mA. The sensitivity will decrease by a factor of \( \frac{500}{50} = 10 \). Thus, the new sensitivity will be:
\[
\frac{x}{10} \, \text{div/mA}
\]
Step 2: Final Answer.
Thus, the sensitivity of the new ammeter will be \( \frac{x}{10} \, \text{div/mA} \).