Step 1: Concept
The shape is determined by VSEPR theory, considering the number of bond pairs and lone pairs on the central atom.
Step 2: Meaning
$BrF_{5}$: Bromine has 7 valence electrons. 5 are used for bonding, leaving 1 lone pair. Steric number $= 5 + 1 = 6$ ($sp^{3}d^{2}$ hybridization). $XeF_{4}$: Xenon has 8 valence electrons. 4 are used for bonding, leaving 2 lone pairs. Steric number $= 4 + 2 = 6$ ($sp^{3}d^{2}$ hybridization).
Step 3: Analysis
For $BrF_{5}$, octahedral geometry with 1 lone pair results in a square pyramidal shape. For $XeF_{4}$, octahedral geometry with 2 lone pairs (placed opposite to each other) results in a square planar shape.
Step 4: Conclusion
The respective shapes are square pyramid and square planar.
Final Answer: (D)