Ferrers diagram rank-metric codes are essential components of the multilevel construction of constant dimension codes for random network coding. This paper aims to construct optimal Ferrers diagram rank-metric codes, focusing on the diagram \([3,3,3,5]\) with rank distance \(3\). We construct an optimal \([[3,3,3,5],6,3]_q\) Ferrers diagram rank-metric code for every prime power \(q\), thereby answering an open problem posed by Etzion et al. in 2016~\cite{Etzion2016}. The construction first builds a \([3\times4,4,3]_q\) MRD code and then proves that the Delsarte dual of its puncturing on the last column contains a \([3\times3,3,3]_q\) MRD code, which comes from semifield codes. We further construct optimal Ferrers diagram rank-metric codes for two infinite families of Ferrers diagrams: the first relies on the \([[3,3,3,5],6,3]_q\) construction and holds for every prime power \(q\), while the second is binary and obtained directly by the puncturing-inclusion construction.

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