Equivalent relation means it should be reflexive, symmetric and transitive. Here we have {1,2,3}.

So for it to be reflexive we should have {1,1},{2,2},{3,3}. This can be done in 1 way.

And any combination of the following 3 groups can be present:- This can be done in 8 ways.

1) {1,2},{2,1}

2) {1,3},{3,1}

3) {2,3},{3,2}

So total 8*1 = 8 ways...but how is the answer 5? Please explain.