High-VHF is channels 7-13, and UHF is 14-51. 52-69 went away a few years ago (auctioned off for other purposes), and 70-83 went away some years before that. Low-VHF isn't used much since the digital transition, but there are some stations using it.
The antenna reacts to the actual broadcast channel (the "Real Channel" column), not the displayed channel ("Virtual Channel"). This is different from the analog days, when there was only one channel on each frequency, and the channel number displayed was the actual broadcast channel. These days, some real and virtual channels are the same, but most are not, as most are using the UHF band. Your virtual channels 2, 4, and 5 are being broadcast on real channels 43, 36, and 31 respectively, so they're UHF now. They kept the familiar (now virtual) channel numbers for loads of reasons, but mainly because they're familiar ('News 4 at 11:00' and such).
As to the HOA, they can frown, but they can't legally stop you from putting up an antenna, even a large one, absent certain other considerations (like a community antenna that gives you everything you want, or certain landmark or historic district type places).
http://www.fcc.gov/guides/over-air-r...n-devices-rule