If you can only have 1 BFF at a time which looks the case here then its extremely messed up. This means now my sim has to be mean with his wife (BFF) to the point they are disliked/enemies so I can make another BFF and then do the same until I get 5 BFF.
The achievement says "Have Had 5 BFF's". I am 99% sure this means you can't have more then 1 bff at the same time, so to make it short you need to get your relationship all the way to max with 1 sim, become bff with them then do mean interactions to become enemy and repeat it 5 times to complete "THE SUPER FRIENDLY" aspiration.
Maxis if this is the case then please look at it.