Short Answer 
In the complex [Fe(CO)5], iron has an oxidation number of 0, indicating no charge due to the neutral CO ligands. Its coordination number is 5, reflecting the five ligands bonded to it, which stabilizes the iron in its elemental state.
Step 1: Determine the Oxidation Number
The oxidation number of an element in a compound reflects its charge. In the complex [Fe(CO)5], we observe that CO is a neutral ligand, which means it does not contribute to the overall charge. Since there are no charges involved in the complex, the sum of the oxidation states must equal zero, leading to the conclusion that the oxidation number of Fe is 0.
Step 2: Identify the Coordination Number
The coordination number of a central metal atom is the total number of ligands bonded to it. In [Fe(CO)5], there are five CO ligands directly attached to the Fe atom. Therefore, the coordination number is equal to the number of ligands, which is 5 in this case. This reflects that Fe is surrounded and stabilized by these five CO ligands.
Step 3: Connect Oxidation and Coordination Numbers
Understanding the connection between oxidation and coordination numbers is crucial. According to Alfred Werner’s postulates, the oxidation state (primary valency) of a metal indicates its charge, while the coordination number (secondary valency) reflects the number of ligands. In [Fe(CO)5], the oxidation number of Fe is 0, indicating that it has not lost electrons, while the coordination number of 5 shows how many donor atoms from the ligands surround the iron atom. This configuration signifies that the iron remains in its elemental state.