Step 1: Configuration of Fe
Fe has \(3d^64s^2\). CO is a strong field ligand, so the electrons rearrange to \(3d^8\), with the \(4s^2\) electrons pushed into \(3d\).
Step 2: Hybrid orbitals
Five CO ligands need five empty orbitals: one \(3d\), one \(4s\) and three \(4p\). This is \(dsp^3\) hybridisation.
The shape is trigonal bipyramidal.
Step 3: Other options
\(sp^3d^2\) and \(d^2sp^3\) would give six ligands. \(sp^3\) would give four. Option (A).
Final Answer:
Fe in Fe(CO)\(_5\) is \(dsp^3\) hybridised, option (A).
\[ \boxed{\text{(A) } dsp^3} \]