Concept:
Resolution of ADC is the smallest change in input voltage that can be detected.
Step 1: Formula
\[
\text{Resolution} = \frac{\text{Voltage range}}{2^n}
\]
Step 2: Given values
\[
n = 10,\quad \text{Range} = 5V
\]
Step 3: Compute denominator
\[
2^{10} = 1024
\]
Step 4: Calculate resolution
\[
\frac{5}{1024} \approx 0.00488V
\]
Step 5: Convert units
\[
0.00488V \approx 4.88\,mV \approx 10\,mV
\]
Conclusion:
\[
\boxed{10\ \text{mV (approx)}}
\]
Final Answer:
\[
\boxed{(A)}
\]