About three to five minutes after the air conditioner shuts down, we hear a boom type sound from the basement. The unit is a Bryant Plus 90 system. Air conditioning was recently serviced and some additional coolant was added.

Sounds like the plenum sheet metal is popping when the blower fan cuts off,, is the filter clean? Did it just start doing this?

I have a similar problem. This problem just started for me after I had replaced my filter.

Yes sounds like ductwork is popping need to listen very carefully, at the furnace, and figure out what piece of sheet metal is popping. Once you determine where it is it will need braced or cross breaked to solve the problem.