Step 1: Understanding the Concept
In \(\text{PCl}_5\) the phosphorus atom is \(sp^3d\) hybridised and the shape is trigonal bipyramidal.
Step 2: Bond Angles and Bonds
There are three equatorial bonds at \(120^{\circ}\) and two axial bonds at \(90^{\circ}\) to the equatorial ones. So two different Cl-P-Cl angles exist.
Step 3: Check the Statements
(A) true. (C) true. (D) true, since five P-Cl sigma bonds are formed.
Step 4: Find the False One
The axial bonds are longer than the equatorial bonds because of greater repulsion. So the statement that all five bonds are identical is false, option (B).
Final Answer:
The false statement is that all five P-Cl bonds are identical in length.
\[ \boxed{\text{(B) }\text{All five P-Cl bonds are identical in length}} \]