The proper way to compare two sets is to use the equals method. I would not worry about performance unless you have proven that this is a part of your code that is causing performance issue (which I doubt). And considering the size of your sets (5 elements) this will be very fast (probably sub millisecond).
keep them as lists, sort them and compare them. (comparable)
will certainly be slower as you will need to copy the elements, sort them and compare.
keep them as sets and compare the hashcode of the sets?
if 2 sets are equal (have the same content) they will have the same hashcode. The reciprocal is not true: 2 sets with different content may have the same hashcode. Also note that for a HashSet
for example, the hashcode is calculated by iterating over all the elements so it is not a free operation.