In the exam, you may expect some concrete vectors given to you and you may go thru the null space calculations as usual. You should try some concrete examples. Any subspace of has dimension at most and all the numbers from to are possible. Let be the standard basis consisting of the columns of identity. To make a two dimesional subspace, you can start with and throw in any three combinations of them to make a list of 5 vectors.
Similar work is done for other dimensions.
For dimension zero, you must take all vectors to be zero. Thus, if you have 5 distinct vectors, then you must have dimension at least 1. The dimension can never be more than 4, since otherwise, you can find 5 independent vectors in . This is known to be impossible. Such a matrix has rank less than or equal to 4 since it has only 4 rows.