In the potential solution observation of the long-sought-after pentazole anion (NO5-), the principal experimental tool used for detection is NMR. However, in two experiments, very different conclusions were reached. To assist in the interpretation, we report predictive level coupled-cluster results for the spin-spin coupling constants and chemical shifts for all of the key species, which include NO3-, N-5(-), HN5, N-3(-), and MeOC6H5N3. In the case of the shifts, an empirical estimate based on the molecule polarity enables comparison of gas-phase and observed values with expected error bars of similar to +/- 10ppm. For the scalar couplings, the evidence is that the solution effects are modest, enabling the gas-phase values (with error bars are similar to +/- 5 Hz) to be accurate. The latter supports the observation of centrally N-15 labeled N-3(-) in the cerium(IV) ammonium nitrate (CAN) solution which could only occur if the pentazole anion had been created in the experiment, yet with too short a lifetime to be observed in NMR.