How can nitrogen achieve +5 oxidation state?
The concept of oxidation states is just that: A theoretical concept. You assign electronegativity values based on one of the numerous scales available, split the bonds heterolytically according to those numbers, and then count electrons.

As such, it is very easy to make a cation like @permeakra stated in the comments that satisfies the octet rule and still gets to state +5 (the molecular cation in question is $\ce{NF4+}$).

There are no $d$ orbitals necessary (which are also theoretical, but slightly closer to reality) to explain how a +5 state is possible.