Aha! The question is misleading because it begins, "According to the balanced reaction below," but in fact the reaction below that is NOT balanced! In order to proceed, we first need to balance it.
DiNitrogen pentaoxide deomposes: N2O5 --> NO2 + O2 Now straight away we perceive that this equation has two nitrogens on the left (reactant side) but only one nitrogen on the right. So let's put a 2 in front of NO2
N2O5 --> 2NO2 + O2
Now the equation has the same number of nitrogens (one times two and two times one) on each side. It also has the same number of oxygens (5) on each side. That is, the equation is balanced. Now we can proceed.
0.00520 moles of N2O5 times 2 moles of NO2 per mole of N2O5 = 0.0104 moles of N2O5 . That is the answer.
Note that we must not write 0.01040 moles of N2O5 because that would have four significant figures and we are only entitled to three.