Why is there no self in the container of the 5 aggregates?

I can see that there is no self to find in the 5 aggregates. But what about their container ? I have a recurrent thought which troubles me : I imagine the 5 aggregates happening within a frame, which is a different one for every living creature. There is this frame, this *perspective*, which is unique for any of us, starts at birth, and ends at death. The five aggregates can only be experienced through that *perspective*. I can't feel what my cat is feeling when I touch it, I can only experience the aggregates appearing inside *my perspective*, not the one of the cat. I don't feel like this is contradicting any buddhist view. The problem is that I don't see how one is suppose not to identify with his own *perspective*. 1) Where is the impermanence in this ? 2) How can identifying a self there can lead to suffering ? 3) Is there a reference about it in the suttas ?