The use of pairs of pseudopure states (POPS) as the basis for nuclear magnetic resonance (NMR) quantum computing is a method recently introduced. The advantage of this approach is its experimental simplicity: each POPS can be prepared in a single experiment with two steps, the first step having two pulses and the second having only one. The POPS method is now demonstrated for a 4-qubit and a 5-qubit system, for which the F-19 and H-1 spectra are first order and all the peaks are completely resolved. The characteristics of the POPS spectra are examined in detail, and the spectra of one of the five available sets of POPS for the 5-qubit system are shown as an illustration. The result of applying a c(4)-NOT quantum logic gate (controlled-NOT gate conditional upon the state of four other qubits) to another set of POPS in the 5-qubit system is also shown.