Is PF5 Polar or Nonpolar?

Answer: PF5 is a nonpolar molecule because when you consider its horizontal and vertical planes electron pulls balance themselves out to achieve a neutral conformation. 

Although the difference electronegativity difference between phosphorus (2.19) and Fluorine (3.98) is large enough to create polar covalent bonds within the structure, the way these bonds are arranged around the central phosphorus cancels out these inequalities. If you slice the molecule in one direction/plane you will see a linear structure similar to that of CO2 (see why CO2 is nonpolar in this article). If you slice the molecule now in the other orthogonal plane/direction you will see a trigonal planar structure similar to that of BF3 (see why BF3 is nonpolar in this article). Since both of these constituent structures are nonpolar, the sum of their parts is also nonpolar.

Another possible question regarding this structure may be the apparent violation of the octet rule on the central Phosphorus atom. When you count up all of the electrons, it seems that the central phosphorus atom shares ten electrons. This kind of configuration can work under the theory of expanded octets which explains this violation by having some electrons participate in bonding via the d subshell found in the third energy level. This means that elements without a third subshell (i.e. all the elements with less protons than Neon) cannot have expanded octets. Although other molecules with expanded octets are rare, they do exist especially as the number of electrons in an element increases.

PF5 Ball and Stick Structure
PF5 Ball and Stick Structure. Created with MolView.
How does PF5 actually behave in nature?

Due to the presence of many extremely electronegative fluorine atoms, the structure is electron-deficient and acts as a Lewis acid. PF5 will as a result of these characteristics will readily undergo hydrolysis even though this is an atypical property for nonpolar molecules.