Step 1: Extrinsic Pathway Initiation.
The extrinsic pathway commences with the leakage of tissue factor (TF), or thromboplastin, into the bloodstream from damaged tissues.
Therefore, the first step corresponds to (C).
Step 2: Clotting Factor X Activation.
In the presence of calcium ions (Ca$^{2+}$) and tissue factor, clotting factor X undergoes activation.
Consequently, the second step is denoted by (D).
Step 3: Active Complex Formation.
Activated factor X, in conjunction with factor V and Ca$^{2+}$, forms the Prothrombinase complex.
Thus, the third step is represented by (E).
Step 4: Prothrombinase Generation.
This complex facilitates the actual synthesis of the Prothrombinase enzyme.
Accordingly, the fourth step is designated as (A).
Step 5: Prothrombinase Activation.
Finally, Prothrombinase becomes activated and catalyzes the conversion of Prothrombin to Thrombin.
Hence, the fifth step is identified as (B).
Step 6: Summary.
The correct sequence of events is (C) → (D) → (E) → (A) → (B).