The correct statement with respect to ${\mathrm{XeF}}_5^{-}$ is There are two non-bonding electron pairs, one above the plane and the other below the plane.

Two non-bonding electron pairs, one above the plane and the other below the plane, are present in the ${\mathrm{XeF}}_5^{-}$ ion. 5 of the 9 electrons available to the core $\mathrm{Xe}$ atom are utilized to create 5 connections with 5 F atoms. The remaining 4 electrons function as 2 lone electron pairs.

Pentagonal bipyramidal shape induces ${\mathrm{sp}}^3{\mathrm{d}}^3$ hybridization of the center $\text{ Xe }$ atom. The pentagonal plane contains the five F atoms. One single electron pair is above the plane, while the other single electron pair is below the plane.

Hence, option C is correct