5. Find the minimum number of sets that can simultaneously satisfy the following three conditions:
(1) Each set contains four elements;
(2) Any two sets have exactly two common elements;
(3) The common elements of all sets do not exceed one.
(2014, China Hong Kong Team Selection Exam)
First, choose two sets from $\{a, b, c, d\}$ and $\{a, b, e, f\}$. It is easy to prove that the number of sets containing both elements $a$ and $b$ does not exceed three. We consider two cases: when there are two sets containing both elements $a$ and $b$, the maximum number of sets satisfying the condition is seven; when there are three sets containing both elements $a$ and $b$, the maximum number of sets satisfying the condition is also seven.