L.H.
My two youngest have birthdays five days apart. We have done shared birthday parties and separate birthday parties. The shared ones are usually larger and if they have separate ones they are usually only with a couple of kids.
We don't do large birthday parties every year for every child. Having four kids that would get too expensive. So they take turns having the big party, and for the kids who don't have the big party, we do separate family parties on the evening of their birthday or something else special for them, like letting them have one or two friends over for a sleepover.
My sister and I have birthdays six days apart. When we were growing up, we didn't have many parties at all, we couldn't afford them. My mom always did something special for us on our own birthday. When we got older and moved away from home, we started celebrating our birthdays together. We would get together whenever convenient and have a nice dinner together.