inorganic chemistry - Why can't NH5 form?

In ammonia a nitrogen atom forms 3 covalent bonds with hydrogen atoms and has one lone pair which can be used in a dative covalent bond with another hydrogen atom to form an ammonium ion. Instead of using both electrons for one dative covalent bond why can't they both individually be used for 2 separate covalent bonds forming NH₅?

Answer

I have pursued such questions regarding the hypervalency of particular molecules before and thus, I would like to provide some insights to the matter.

A common superficial answer that one can provide to answer the question is that there are ten electrons around the central nitrogen atom in $\ce {NH5}$ and thus, it cannot exists based on the octet rule. And we do know that the octet rule must be strictly abided by for the period 2 elements.

However, let us look at the deeper reasons why period 2 elements behave in this way by looking at the characteristics of hypervalent molecules.

One very crucial reason why particular hypervalent molecules and molecular ions, such as $\ce {PCl5}$ and $\ce {SO4^{2-}}$, can exist is due to the presence of electronegative ligands around the central atom which can draw electron density away, reducing the inter-electronic repulsion in the molecule and hence, increasing the stability of the molecule significantly. Due to the significant ionic character resulting from forming multiple polar covalent bonds, there is actually significant ionic character within the molecule. Computational studies have shown that some of these central atoms are, in fact, bearing significant charge, with some even having a greater charge than +1. Although you may expect that central atoms in hypervalent molecules have more than 8 electrons, the reality is that they likely have less! This was shown in a study conducted by Noury, Silvi and Gillespie.^[1] This goes to show how electron-withdrawing are the electronegative ligands.

Another important factor to consider is sterics. Simply put, we cannot put multiple large atoms around a small atom. Atoms of the elements of period 2 may not have reached the "critical size" for it to accommodate more atoms around it while period 3 elements seem to be able to accommodate more atoms much more easily. This is the likely reason why the molecule $\ce{NF5}$ does not exist. While the electronegative fluorine ligands may help to reduce electron density accumulating in nitrogen, the space constraints simply are too limiting. You can read more about the molecule and its associated instability at its Wikipedia page. The references provided on the page are also very insightful.

I hope it is now clear why $\ce {NH5}$ cannot exists based on considerations of the two factors above.

References

1. Noury, S.; Silvi, B.; Gillespie, R. J. Chemical Bonding in Hypervalent Molecules:  Is the Octet Rule Relevant?. Inorg. Chem. 2002, 41 (8), 2164–2172. DOI: 10.1021/ic011003v.