Step 1: What resolution really means.
Resolution is simply the smallest step size the ADC can represent, that is, how much the analog input voltage must change before the digital output code changes by one count.
Step 2: Split the full range into equal steps.
A 10-bit converter produces $2^{10} = 1024$ distinct output codes, so the 5 V input range is effectively sliced into 1024 equal steps. Each step size is $\dfrac{5\text{ V}}{1024} \approx 4.9\text{ mV}$.
Step 3: Match this to the closest practical answer.
Among the given choices, 100 mV, 0.5 V and 1 V are all far too coarse for a 10-bit converter, since they would only need a handful of bits to represent. The value in the low millivolt range fits only the smallest listed option.
\[ \boxed{10\text{ mV}} \]