A student lists five statements about hybridisation. (i) In $\text{PCl}_5$, phosphorus is $sp^3d$ hybridised, and the two axial bonds are longer than the three equatorial bonds. (ii) In $\text{SF}_6$, sulphur mixes one 3s, three 3p and two 3d orbitals. (iii) In ethyne, each carbon uses two $sp$ orbitals for σ bonds and two 2p orbitals for π bonds. (iv) In ammonia, nitrogen is $sp^2$ hybridised, with its lone pair in a p orbital. (v) Only half-filled orbitals can take part in hybridisation. How many of these statements are correct?