5. There are 7 points on a plane, with no three points collinear. Using these points as vertices to form triangles, such that any two triangles have at most one common vertex and no common edges. Then the maximum number of triangles that can be formed is ( ).
(A) 3
(B) 7
(C) 21
(D) 35
5.B.

On the one hand, 7 points can connect to form $\frac{7(7-1)}{2}=21$ edges, and each edge can belong to at most one triangle, so 21 edges can form at most 7 triangles; on the other hand, with 1, 2, $\cdots$, 7 as vertices, 7 triangles that meet the conditions can actually be constructed. For example, by rotating the triangle in Figure 3 seven times clockwise, we can obtain the triangles
$$
\begin{array}{l}
(1,2,4),(2,3,5),(3,4,6),(4,5,7), \\
(5,6,1),(6,7,2),(7,1,3) .
\end{array}
$$