1. Find the central atom and count valence electrons

Both species have iodine as the central atom.

• Iodine has $7$ valence electrons.
• Each chlorine forms one single bond with iodine.

2. Structure of $ICl_5$

For $ICl_5$:

• Central iodine forms $5$ bonds with $5$ chlorine atoms.
• So iodine uses $5$ electron pairs in bonding.
• Since iodine starts with $7$ valence electrons, after forming $5$ bonds, one lone pair remains on iodine.

Thus, around iodine there are: $5\text{ bond pairs} + 1\text{ lone pair} = 6\text{ electron pairs}$

According to VSEPR, $6$ electron pairs give an octahedral electron pair geometry. With one lone pair, the molecular shape becomes square pyramidal.

So, $ICl_5 \text{ is square pyramidal.}$

3. Structure of $ICl_4^-$

For $ICl_4^-$:

• Iodine has $7$ valence electrons.
• Negative charge adds $1$ more electron.
• Total on iodine side effectively becomes $8$ electrons.
• It forms $4$ bonds with $4$ chlorine atoms.

So around iodine:

• $4$ bond pairs
• Remaining electrons give $2$ lone pairs

Hence total electron pairs around iodine are: $4\text{ bond pairs} + 2\text{ lone pairs} = 6\text{ electron pairs}$

Again, electron pair geometry is octahedral. With two lone pairs placed opposite each other, the molecular shape is square planar.

So, $ICl_4^- \text{ is square planar.}$

4. Check the options

• A: $ICl_5$ square pyramidal and $ICl_4^-$ square planar ✅
• B: $ICl_5$ trigonal bipyramidal and $ICl_4^-$ tetrahedral ❌
• C: $ICl_5$ square pyramidal and $ICl_4^-$ tetrahedral ❌
• D: Both are isostructural ❌

5. Final answer

The correct option is: $\boxed{A}$

6. Comparison with stored correct answer

Stored correct answer: $A$

My derived answer: $A$

They match.