Easiest unsolved case of reconstruction conjecture

We spent some time thinking about reconstruction conjecture and got into a conclusion that no one yet solved a simple case as follows.

You have a graph composed of two parts X and Y. In X you have n vertices, in Y you have 2 vertices only. Vertices in Y are connected to X such that all vertices in X have degree 5 and all vertices in Y have degree 4.

So final graph has only two values of degrees, 4 and 5. It's know that when a graph is regular, it can be reconstructed. Here there are only 2 vertices of different degree, nonetheless the problem becomes harder. In more general case you have 2 vertices of degree a and n vertices of degree a+1, but it seems to be much harder to reason about.