To determine the most intelligent child based on the provided information, let's summarize the relationships between the children:
\(A\) is less intelligent than \(B (A < B)\).
\(C\) is less intelligent than \(D (C < D)\).
\(A\) is less intelligent than \(C (A < C)\).
\(A\) is more intelligent than \(E (A > E)\).
Now let's combine this information:
\(A < B\)
\(A < C < D\) (since \(C\) is less intelligent than \(D\), and \(A\) is less intelligent than \(C\))
\(A > E\)
Therefore, the hierarchy of intelligence from least to most intelligent is:
\(E < A < C < D\).
Since \(B\) is more intelligent than \(A\), but there is no direct comparison between \(B\) and \(D\), we know the hierarchy of \(A, C,\) and \(D\) but not between \(B\) and \(D\).
From the given information, \(D\) is the most intelligent child.
So, the correct option is \((C): D\).