Every once in a while there will be a sound like a release go air pressure. It happens every morning at 5:30-odd... What is this and how do we fix it?

Hmmmm...

By your limited description I can only guess that the toilet flapper may not be sealing properly. Here, I would suggest taking some dark food coloring and dripping about 20 drops into the toilet TANK only and then check the toilet BOWL every 10 minutes or so for a couple hours and see if the colored water shows up in the toilet bowl. If colored water shows up in the toilet bowl then the flapper is defective and needs to be replaced....UGH!!

Try the test I suggested and post back with the result, OK?

Mark

Describe the noise in detail. Do you live in an apartment house? Are there any unit is over you? We need more details! Back to you, Tom