Total number of bonds in PCl₅ which are at 90° to each other, is

Hybridization of PCl₅ is sp³d hybridization and its shape is trigonal bipyramidal geometry. There are 5 P-Cl sigma bonds are formed in which three P-Cl atoms are equatorial bonds that lie in one plane at an angle of 120⁰. Rest of two P-Cl atoms are axial bonds that are at right angle to the plane of equatorial bonds that is one above and one below the plane. 
As one axial bond is at right angle to 3 equatorial bonds, there are two axial bonds-so total 6 right angle bonds are there in PCl₅.

$\text{ Total six }{\mathrm{Cl}}_{\mathrm{Ax}}-\mathrm{P}-{\mathrm{Cl}}_{\mathrm{eq}}\text{ bonds are at }{90}^{\circ }\text{ to each other. }$