I admire you sense of adventure with such an itin (and with 4 travelers). I had to look up BJM (It is Burundi's only international airport and the only one with a paved runway.)

There is a good chance with 5 hour connection you can retrieve your carry-on at IAD (but on onward flight on ET will complicate that - you will need to ask ET, not UA))
What was your Boarding Group number?
Not checking-thru bags if overnight / >12 hours is standard UA policy (with a few exceptions)