A.G.
Some babies do not sleep through the night until they're almost a year. My First one slept though the night early, but my second child is another story.
Since the baby is only 5 mos, you have time to learn new techniques. Have you tried putting rice cereal in the formula or the breast milk? It fills the belly.
Also the baby is old enough to take solid foods, have you tried rice or oatmeal for dinner and then a bottle for bed?
I gave my son a bottle in the middle of the night til he was 1.
Try some of the ideas and give the ideas some time- something will click.
Have you tried White noise?