You are nursing, right? Then it's easy :)
You might think I'm being flip, but I'm not. At 4 months, your baby doesn't expect to get up and walk around all the time, and when you are nursing you don't have to worry about getting bottles through security, warming bottles on the plane, etc.
Here are my recommendations:
-Get a window seat. Then you only have to worry about accidentally flashing someone on one side while nursing. If you are flying with another adult, put that person in the middle seat and you'll have a lot of privacy.
-Nurse during takeoff and landing. That will make sure the baby's ears adjust. Don't rely on a pacifier. You have to swallow to pop your ears, not just suck.
-I carried my baby in a ring sling on the plane. I used it when I was sitting, because it helped to give my arms a break from holding the baby, plus I used it like a light nursing blanket over my shoulder and the baby for privacy/modesty when nursing.
-a handful of onsies for the baby (for this long of a flight, I'd take 4, more if your baby is a spitter), a light blanket, and twice as many diapers as you think you will need.
-in your carry-on, take an extra set of clothes for you! Then when the baby spits up on you, you won't have to sit in a bad smelling shirt for 5 more hours :).
-some colorful, relatively quiet toys - rattles are fine, but out of courtesy for your neighbors, please leave the talking Elmo at home unless he has an off switch that you plan to use. I always liked toys that I could hook to strings of those plastic rings that link together, because I hooked the top ring to my ring sling so when baby threw/dropped the toy, it couldn't go too far. If you plan to take a car seat, you can also hook the rings onto a car seat strap.
-many planes have changing tables that fold down in the bathroom, but not all. So change the baby immediately before you get on the plane. I've always been able to find a spot to change diapers, even when there isn't an official changing table, but it is harder on the plane.