Step 1: Identify the ligands present in the complex.
The complex is
\[
[\mathrm{Fe(CO)_5}]
\]
The ligand present is carbon monoxide, denoted by \( \mathrm{CO} \).
In coordination nomenclature, \( \mathrm{CO} \) is named as carbonyl.
Step 2: Count the number of ligands.
There are five carbonyl ligands attached to iron.
Therefore, the ligand part of the name becomes:
\[
\text{pentacarbonyl}
\]
Step 3: Determine whether the complex is neutral, cationic, or anionic.
The complex
\[
[\mathrm{Fe(CO)_5}]
\]
has no overall charge shown, so it is a neutral complex.
For neutral complexes, the metal name is written in its normal form, so we use:
\[
\text{iron}
\]
and not
\[
\text{ferrate}
\]
because “ferrate” is used for anionic complexes.
Step 4: Determine the oxidation state of iron.
Each carbonyl ligand \( \mathrm{CO} \) is a neutral ligand.
Let the oxidation state of iron be \( x \).
Since the whole complex is neutral:
\[
x + 5(0) = 0
\]
\[
x = 0
\]
So the oxidation state of iron is:
\[
\mathrm{0}
\]
Step 5: Write the full name in IUPAC style.
Thus, the name is:
\[
\text{pentacarbonyliron(0)}
\]
Step 6: Eliminate the incorrect options.
Options containing “ferrate” are incorrect because the complex is not anionic.
Options with oxidation states \( +2 \) or \( +3 \) are also incorrect because carbonyl is neutral and the complex has overall charge zero.
Step 7: Final conclusion.
Hence, the IUPAC name is
\[
\boxed{\text{Pentacarbonyliron(0)}}
\]
Therefore, the correct option is
\[
\boxed{(3)}
\]