electrons - Negative energy levels in the diagram for a hydrogen atom

The higher the number of the shell (n), the higher is the energy level of the electron. However, why was it necessary to have negative values. So for example, when $n=1$, the energy could be $5 eV$ and for $n=2$, $6 eV$... having positive values could also have supported the idea that as $n$ increases, energy of electron increases. What is the point of having negative numbers, does it somehow aid calculations?

Answer

We say that a free, unbound electron has zero energy (that's convention, you could just as well put another number there). This means that the level $n = \infty$ is fixed at $E_\infty = 0 \text{eV}$. Since the other levels lie lower, i.e. possess less energy, this forces all other bound states to have negative energies - which then represent that we need to add energy to make the bound state free, which corresponds to raising its energy to zero.