Using a large collection of near-infrared spectra (2.5-5.4 um) of Galactic HII regions and HII region-like objects, we perform a systematic investigation of the astronomical polycyclic aromatic hydrocarbon (PAH) features. 36 objects were observed by the use of the infrared camera onboard the AKARI satellite as a part of a directers time program. In addition to the well-known 3.3-3.6 um features, most spectra show a relatively-weak emission feature at 5.22 um with sufficient signal-to-noise ratios, which we identify as the PAH 5.25 um band previously reported. By careful analysis, we find good correlations between the 5.25 um band and both the aromatic hydrocarbon feature at 3.3 um and the aliphatic ones at around 3.4-3.6 um. The present results give us convincing evidence that the astronomical 5.25 um band is associated with C-H vibrations as suggested by previous studies and show its potential to probe the PAH size distribution. The analysis also shows that the aliphatic to aromatic ratio of I(3.4-3.6)/I(3.3) decreases against the ratio of the 3.7 um continuum intensity to the 3.3 um band, I(3.7 cont)/I(3.3), which is an indicator of the ionization fraction of PAHs. The mid-infrared color of I(9)/I(18) also declines steeply against the ratio of the hydrogen recombination line Bralpha at 4.05 um to the 3.3 um band, I(Bralpha)/I(3.3). These facts indicate possible dust processing inside or at the boundary of ionized gas.