Prove that we can have a graph with 15 vertices that every vertex is exactly connected to 5 another vertices

Imagine a city that has 15 public phones. Is it possible to connect them to each other with some cables in case that every phone must connect to exactly 5 another phone. I tried to draw this graph with 15 vertices but

I could just fill 14 vertices and the last vertex 's degree was 4.

Is there a strong way to prove that it's possible?

• Is there always a graph with $n$ nodes, such that each node is connected to $k<n$ other nodes (for any choices of $n$ and $k$ that meet the criterion you stated)? – DreiCleaner Jun 16 '20 at 15:13
• @DreiCleaner It is possible if and only if $n \cdot k$ is even. – N. S. Jun 16 '20 at 15:56