In matching a vertex can be present at most once.
Among the vertex 1, 2, 3, 4, 5. We are going to miss the one vertex either it is 1, 3 or 5. In the image 3 is absent in matching.
Now, we are left with 5 more vertices, With 5 vertices we can't have 3 pairs of different vertices. We can only have 2 pairs of different vertices.
Ans: $\left | M \right |$ = 4