What we need to ask is the number of A, which is equivalent to the number of proper subset sets that do not belong to {1, 3,5} but {1, 2,3,4,5}, that is, the number of proper subset of {2,4}.
It can be seen that the proper subset of {2,4} is φ, {2}, {4}, which is C.
in other words
{ 1,3,5}∪Φ={ 1,3,5}
{ 1,3,5}∪{2}={ 1,2,3,5}
{ 1,3,5}∪{4}={ 1,3,4,5}
These three sets are proper subset of {1, 2, 3, 4, 5}.
If you have any questions, please ask.