Have you tried to nurse him?
Nurse him before bed, and during the night.
Know, a baby's hunger cues.
One thing, that needs to be noted is:
That a pacifier or rocking a young baby, does not.... "replace" the need for feedings, at night. A baby wakes, because ALSO they are hungry.
A baby, needs to be nursed at night too.
At 5.5 months old, baby is still very young. And a growth-spurt will make any baby, NEED to feed, for biological reasons... much more and more frequently and more often and just, more. Or it can be that baby is ALSO teething.
A hungry baby, will not soothe.
Nor will a pacifier soothe a hungry baby.
Or sometimes a baby gets gas, pains. Their digestive system is still, developing.
A baby needs to be nursed, on-demand. And often times, "cluster feeding" occurs, which is normal, and a baby will then need to feed even every single hour.
Does he nap during the day? Infants often nap, 2-3 times a day.
My kids as babies, nursed about every 2 hours, or less when hitting growth-spurts. And this was, day AND night. And they had, GINORMOUS appetites. Feedings on a "schedule" does not address, a baby's needs, thus feeding on-demand is recommended. Because, a baby's appetites, changes every day. It is not the same everyday.
Per our Pediatrician, for the 1st year, a baby's PRIMARY source of nutrition is from breastmilk or Formula. Solids is not as nutritionally dense. And to feed on-demand. The first year is a building-block period, for development.