A mineral that is scratched by apatite (hardness 5) but not by calcite (hardness 3) must have a hardness value between 3 and 5. This means the mineral's hardness could be 4 or 5. Since it is not scratched by calcite, it cannot be 3 or lower.
So the only appropriate hardness value from the options provided is:
4
Therefore, the answer is 4.