The correct option is C sp, sp3 and sp2
Short version: C1 is sp hybridised, C3 is sp3 hybridised and C5 is sp2 hybridised.
Long version:
In the case of hybridisation of carbon, the easiest way is to look at the number of atoms it is bonded with or the presence of double or triple bonds
If the carbon is bonded to 4 other atoms, it is sp3 hybridised since sp3 hybridisation gives rise to 4 hybrid orbitals of equal energy levels which can participate in bonding. This allows carbon to form 4 σ bonds.
If the carbon is bonded to 3 other atoms, it is sp2 hybridised giving rise to 3 hybrid orbitals and one p-orbital. This allows the formation of 3 σ bonds and 2 π bonds i.e. one double bond and 2 single bonds.
The reasoning for sp hybridisation similar. Just look for a triple bond.