We continue our recent work of characterizing the plasma content of high-redshift damped and sub-damped Lyman-alpha systems (DLAs/sub-DLAs), which represent multi-phase gaseous ( proto) galactic disks and halos seen toward a background source. We survey N V absorption in a sample of 91 DLAs and 18 sub-DLAs in the redshift range 1.67 < z(abs) < 4.28 with unblended coverage of the N V doublet. Our dataset includes high-resolution (6-8 km s(-1) FWHM) quasar spectra obtained with VLT/UVES and Keck/HIRES, together with medium-resolution (approximate to 40 km s(-1) FWHM) quasar spectra from Keck/ESI. In DLAs, we find eight secure N V detections, four marginal detections, and 79 non-detections, for which we place 3 sigma upper limits on the N V column density. The detection rate of N V in DLAs is therefore 13(-4)(+5)% . Two sub-DLA N V detections are found among a sample of 18, at a similar detection rate of 11(-7)(+15) %. We show that the N V detection rate is a strong function of neutral-phase nitrogen abundance, increasing by a factor of approximate to 4 at [N/H] = [N I/ H I] > -2.3. The N V and C IV component b-value distributions in DLAs are statistically similar, but the median b(N V) of 18 km s(-1) is narrower than the median b(O VI) of approximate to 25 km s(-1). Some similar to 20% of the N V components have b < 10 km s(-1) and thus arise in warm, photoionized plasma at log (T/K) < 4.92; local sources of ionizing radiation (as opposed to the extragalactic background) are required to keep the cloud sizes physically reasonable. The nature of the remaining approximate to 80% of (broad) N V components is unclear; models of radiatively-cooling collisionally-ionized plasma at log (T/K) = 5.2-5.4 are fairly successful in reproducing the observed integrated high-ion column density ratios and the component line widths, but we cannot rule out photoionization by local sources. Finally, we identify several unusual DLAs with extremely low metallicity (< 0.01 solar) but strong high-ion absorption (log N(N V) > 14 or log N(O VI) > 14.2), which present challenges to either galactic inflow or outflow models.