[eglaud]

Looking at the TeF₅^- molecule it is clear that the normal sp³ bond won't cut it. I am aware that the Te atom forms an sp³d² bond, but why? I can see that since 6 bonds are needed, and the d² seems to be used to add the two needed, but how does this work, in terms of simple chemistry? We typically use energy diagrams for this. Thanks

[AdiDex]

Recall the definition of Hybridization

hybridisation is the concept of mixing atomic orbitals into new "equal" no. hybrid orbitals (with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to form chemical bonds in valence bond theory. (Reference to wikipedia )

You need 6 orbitals --> 5 for sigma bonds (Te-F bonds) and one for Lone pair of electrons . Molecule tends to be in this shape because this is the best orientation for their orientation .
You may get confused ,but this is the reality that Hybridisation is just a Hypothetical model , which is use to predict the shape of a molecule . Actually there is no such Hybrid orbitals which exist in reality . Go through this text .