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The 5~24VDC operating range just means the controller can work with voltage within this range. For driving 24V AC solenoids, as I mentioned in the post, 9V DC is the optimal as it provides just the right amount of holding current (typical 24V AC solenoid resistance is about 35 to 45 ohms).
In case you want to run 12VDC solenoids, or 24VDC solenoids, you can do so with OpenSprinkler DC by changing to use a 12VDC (or 24VDC) power supply. So you are basically matching the power supply with your solenoid specification. Still, I suspect that even 12VDC or 24VDC solenoids would work just fine with a 9VDC power adapter, because usually once energized these solenoids can stay on at a much lower voltage, and the boost converter will help energize them initially.
You are right that 5V is below the starting voltage of 7805. However, you can actually plug in a USB cable (5V) to OpenSprinkler DC’s USB port to power it, and this bypasses 7805. The circuit design has a diode that back feed the 5V to the COM wire so you can power solenoids using a USB adapter. I’ve tested sprinkler solenoids and it works just fine. In short, you can power 24V AC solenoids with just a USB cable plugged into the USB port. This sounds a bit wild. I don’t want to advertise this because it’s not fully tested and I don’t know how reliably it is. At 5V the holding current is only about 150mA, which is technically below spec, but it seems to work ok.