Question

Nitrogen do not have d orbital so how can it show +5 oxidation state?

Answer 1

Nitrogen is a 2nd period element and its a chemical sin to put more than 8 valence electrons around nitrogen as there are only four orbitals (s.p.p.p) availble in the 2nd energy level. 
Oxidation number is a number that has no significance to structures. Its designated by noting the charge on the atom after theoritically giving the bonded electrons in a bond to the more electronegative element. 
In NO3 - we have nitrogen forming 4 covalent bonds but the oxidation state is +5.