Step 1: Identify the central atom and its group.
In $SbF_5$ the central atom is antimony, which sits in group 15, so it brings $5$ valence electrons.
Step 2: Count the things attached.
Five fluorine atoms are bonded to antimony, each forming one single bond, so there are $5$ bonding regions.
Step 3: Find lone pairs by electron bookkeeping.
Each $Sb-F$ bond uses one antimony electron, so $5$ electrons go into bonds. That uses all $5$ valence electrons, leaving $0$ lone pairs on antimony.
Step 4: Get the steric number.
Steric number $=$ bonding regions $+$ lone pairs $= 5 + 0 = 5$. A steric number of $5$ means $sp^3d$ hybridisation.
Step 5: Apply VSEPR for five clouds, zero lone pairs.
Five electron clouds with no lone pair always spread into the trigonal bipyramidal shape to keep repulsion lowest.
Step 6: Describe and conclude.
Three fluorines sit in the equatorial plane $120^\circ$ apart and two sit axially at $90^\circ$, giving a trigonal bipyramidal molecule.
\[ \boxed{\text{Trigonal bipyramidal (option D)}} \]