I got one of those buckets a few years ago as a gift. It looks like a 7 gallon bucket with a sit-on lid, with a foam liner and lid inside the bucket. Some were sold at walmart, had something that looked like fish on them. Others had some beer brand on them. Some were camo. I found others too, free ones. The foam liner will fit a 5 gallon bucket, may have to trim the top with a blade for a lid to fit onto the bucket.
Academy Sports has a Lid that fits a 5 gallon bucket for about $2.00, it has a hole for the air hose, a slot for the air pump to hook on and a vented lid to get to the minnows.
I went to a warehouse clearance and found some min-o-life foam buckets that are made to fit the steel wire frame, with lid for a dollar. They had 7. The minnow net with the float handle for 35 cent, they had 9. A few other things but one of my good days shopping.