The shape/structure of $$[XeF_5]^-$$ and $$XeO_3F_2$$, respectively are:

We begin with the anion $$[XeF_5]^-.$$

For VSEPR calculations we first count the electrons present on the central atom in the following standard way:

Steric number = $$\dfrac{\text{valence electrons of the central atom} + \text{electrons contributed by all monovalent ligands} - \text{charge}}{2}.$$

• Xenon belongs to group 18, so it possesses $$8$$ valence electrons.
• Five fluorine atoms are monovalent; each contributes one electron to a σ-bond, giving $$5$$ electrons.
• The ion carries a charge of $$-1,$$ which adds one more electron.

Putting these values into the formula, we get

$$\text{Steric number}=\dfrac{8+5+1}{2}= \dfrac{14}{2}=7.$$

So around xenon there are $$7$$ electron pairs: $$5$$ bonding pairs (one for every Xe-F σ-bond) and $$2$$ lone pairs. For steric number 7 the ideal electron-pair arrangement is pentagonal bipyramidal. To minimise repulsion, both lone pairs occupy the two axial positions, leaving the five fluorine atoms in a single equatorial plane. Hence the observable molecular geometry is

$$\boxed{\text{pentagonal planar}}.$$

Now we examine $$XeO_3F_2.$$

Here xenon is bonded to three oxygen atoms and two fluorine atoms, giving a total of five σ-bonds.

• Xenon again supplies $$8$$ valence electrons.
• Two Xe-F σ-bonds use one electron each from xenon, consuming $$2$$ electrons.
• Each oxygen is double-bonded to xenon. A double bond contains one σ and one π pair; the σ part consumes one electron from Xe, the π part consumes a second electron. Thus the three Xe=O bonds together take $$3\times2=6$$ electrons from xenon.
• Altogether xenon uses $$2+6=8$$ of its electrons in bonding, exhausting its valence shell and leaving $$0$$ electrons for lone pairs.

Therefore

number of σ-bonds $$=5,\qquad \text{number of lone pairs}=0,$$

so the steric number equals $$5.$$ The electron-pair geometry for steric number 5 is trigonal bipyramidal, and because there are no lone pairs, the molecular shape is also

$$\boxed{\text{trigonal bipyramidal}}.$$

Thus the geometries are pentagonal planar for $$[XeF_5]^-$$ and trigonal bipyramidal for $$XeO_3F_2.$

Comparing with the choices given, Option A lists these two shapes in the required order.

Hence, the correct answer is Option A.