Hmm, not sure if it's "normal", I think every sibling relationship has it's own dynamic.

My kids are two years younger than yours, but DD is up and down as to letting DS play with her. She sits on the floor with her books and sometimes will give him one, other times will have a tantrum just because he's near her. She sometimes takes things from him that she hasn't looked at for days, because suddenly she needs it. And the toy I give him next. And the next one. He can't have anything. She's slowly learning that if she wants something he had, she needs to ask for it and give him something else so he's not left with nothing and she's not just snatching all the toys.

My brother and I had a fantastic relationship. Similar age gap, 2.5 years. We played really well together, most activities were done together, but there were definitely times iv wanted my own space. My Mum thought maybe it was because he'd always had someone there to play with but I was used to those 2.5 years doing my own thing.

Then there's DH and his sister. Got along like a cat and a dog, fighting all the time and rarely playing well. No idea why it was different for them, it just was!