This spectrum has several interesting features. First, hydrogens A, B & C are clearly different, and are spin-coupled to each other. Hydrogens B & C are geminally related, whereas A is oriented to B & C in a vicinal manner. Since J_AB and J_BC are similar, the H_B signal is a broad triplet. Although hydrogens D & E might seem identical at first glance, they are diastereotopic, and should therefore have different chemical shifts. The DE geminal coupling constant is 11.7 Hz, so each of these hydrogens appears as a doublet of doublets.
The splitting of the H_A signal is complex and not immediately obvious. The diagram on the right shows the consequences of the four operating coupling constants.