1. Use VSEPR to determine shape of each species
   Square pyramidal geometry generally arises for steric number $6$ with arrangement $AX_5E$: $\text{6 electron pairs} = 5 \text{ bond pairs} + 1 \text{ lone pair}$ This gives an octahedral electron-pair geometry and a square pyramidal molecular shape.

We now check each species.

2. $\mathrm{PF_5}$
   Central atom: $P$
   Valence electrons on $P = 5$
   It forms $5$ bonds and has no lone pair.

So it is: $AX_5$ Geometry = trigonal bipyramidal, not square pyramidal.

❌ Not counted.

3. $\mathrm{BrF_4^-}$
   Central atom: $Br$
   Valence electrons on $Br = 7$, plus $1$ extra for negative charge $\Rightarrow 8$ electrons.

It forms $4$ bonds, leaving $2$ lone pairs on Br. So: $AX_4E_2$ Electron pair geometry = octahedral
Molecular shape = square planar.

❌ Not counted.

4. $\mathrm{IF_5}$
   Central atom: $I$
   Valence electrons on $I = 7$
   Forms $5$ bonds, leaving $1$ lone pair. So: $AX_5E$ Electron pair geometry = octahedral
   Molecular shape = square pyramidal.

✅ Counted.

5. $\mathrm{BrF_5}$
   Central atom: $Br$
   Valence electrons on $Br = 7$
   Forms $5$ bonds, leaving $1$ lone pair. So: $AX_5E$ Molecular shape = square pyramidal.

✅ Counted.

6. $\mathrm{XeOF_4}$
   Central atom: $Xe$
   Valence electrons on $Xe = 8$.

Around Xe: one $Xe=O$ double bond, four $Xe-F$ single bonds, and one lone pair.
In VSEPR, the double bond counts as one electron domain. Thus total electron domains around Xe: $1(O) + 4(F) + 1(\text{lone pair}) = 6$ So: $AX_5E$ Molecular shape = square pyramidal.

✅ Counted.

7. $\mathrm{ICl_4^-}$
   Central atom: $I$
   Valence electrons on $I = 7$, plus $1$ extra due to charge $\Rightarrow 8$.

Forms $4$ bonds, leaving $2$ lone pairs. So: $AX_4E_2$ Molecular shape = square planar.

❌ Not counted.

8. Total number of square pyramidal species

Square pyramidal species are:

• $\mathrm{IF_5}$
• $\mathrm{BrF_5}$
• $\mathrm{XeOF_4}$

Hence, total number is: $\boxed{3}$

9. Comparison with stored correct answer
   Stored correct answer = $3$
   Derived answer = $3$

So the answer agrees with the stored correct answer.