To not know what to do with this baby inset seat to car seat?

[hupppj]

5 month old dd and when I take it out there’s gaps between the side of her head and the seat?

Yes I think that's normal - now she's older she will have a stronger neck to hold her own head straight while she's awake. If she falls asleep her head will fall to the side and rest against the seat.

Are you removing the baby insert at the right height/weight point? I think you're generally supposed to go by height and weight instead of age for car seats.

It's hard to advise without knowing the seat and the size of your child, but often you can keep it in if you think they still fit better with it in. Ask the manufacturer for advice or check the manual.