1. Assign the oxidation number of oxygen (-2) to each oxygen atom in the compound. There are three oxygen atoms, so the total contribution from oxygen is 3 * (-2) = -6.
2. Assign the oxidation number of hydrogen (+1) to each hydrogen atom in the compound. There is one hydrogen atom, so the contribution from hydrogen is 1 * (+1) = +1.
3. Let x be the oxidation number of nitrogen.
4. The sum of the oxidation numbers of all atoms in a neutral compound must be zero. Therefore, we can write:
```
x + (-6) + (+1) = 0
```
5. Solving for x, we get:
```
x = +5
```
Therefore, the oxidation number of nitrogen in NHO3 is +5.