Which of the following statements is/are correct regarding IF₅ molecule?

(I) There is only one lone pair present in the central atom of molecule.

(II) All $\angle \mathrm{FIF}$ angles are identical.

(III) All $\angle \mathrm{FIF}$ angles are less than $90°.$

(IV) There are five electron pairs in IF₅ molecule.

Structure of IF₅ is given below. 

In IF₅, there are four equatorial bonds and each of F atom has three lone pairs of electron. One F atom present at axial along with one lone pair of electron of Iodine.

Therefore, statement (I) is correct.

Theoretically there is $90°$ angle between axial and equatorial bonds but due to presence of a lone pair of electron, all angles of F-I-F are identical and is equal to $89.5°.$ Therefore, statement (II) and statement (III) is correct.

There are six electron pairs in IF₅, five are the bond pairs and one is the lone pair. Therefore, hybridization of IF₅ is sp³d² whose geometry is octahedral and shape is square pyramidal. 

Therefore, statement (IV) is incorrect.