Hi Katie. So sorry your betta is sick like this. You said you haven't been feeding him but when you did feed him, would he eat? Has he had this lump for only five days or has it been steadily growing larger over several weeks?
It's definitely not dropsy because there are no raised scales or general bloating. Rather, it looks as if he has either a tumor, as Callistra said, or a problem in his swim bladder. Does he have trouble swimming or buoyancy problems?
One other possibility is a fatty deposit because of a high protein diet. If this is the case, keeping him in a high dosage of epsom salts and carefully monitoring the fat content of his food may decrease the size of the deposit. However, if it is a tumor there is nothing that can be done except to make him comfortable. :( Unfortunately, there is no way of knowing if it is a deposit or a tumor. Because of that reason, I would suggest keeping him in a smaller hospital tank with 3 tsps of epsom salts and tannins, such as Indian Almond leaves or naturally dried and clean oak leaves.