Step 1: Understanding the Concept
Bromine has 7 valence electrons. Five are used in bonds with fluorine, leaving one lone pair.
Step 2: Geometry
There are 5 bond pairs and 1 lone pair, so \( sp^3d^2 \) hybridisation and octahedral electron geometry.
Step 3: Shape
With one lone pair the shape is square pyramidal, option (C).
Final Answer:
BrF5 has a square pyramidal shape.
\[ \boxed{\text{(C) }\text{Square pyramidal}} \]