In the reaction we see that the ratio of N2 moles to O2 moles is 1:2. If we use the available (given) moles of these two gases, we see that the O2 is the limiting reactant and will all be used up. This will produce 5 moles of NO2 and use up 2.5 moles of the N2, leaving 1.5 moles unreacted.
So, the contents in the reaction vessel will be: 5 moles of NO2 and 1.5 moles of N2