Prove that for every number $n\geq 5$ there exists a graph with $n$ vertices, all of which have degree $4$.

I'm not sure how to do this. I've tried a few things. I was thinking induction, the base case is $K\_5$ and then I assumed the result was true from some number $k$ and then considered $k+1$ vertices, but I don't know how to proceed.

The other approach I had was to construct the graph it asked for: Consider a cycle with $n$ vertices, all of the vertices have degree $2$. Now connect each vertex by an edge to the neighbor of the vertices they're adjacent to. This process works for all $n$, but I don't know how to show that it terminates.

Any solutions or help is greatly appreciated.