The equivalence classes are
{....,−4,1,6,11,...},{...,−3,2,7,12,...},{....,−2,3,8,13,...},{....,−1,4,9,13},{...,0,5,10,15,...}
So the given relation partitions the set into 5 equivalent classes.
Also, any two equivalent classes are either equal or disjoint.
So both the statements are correct.