SirHumphreyAppleby: Assuming you're using the LD2410, these will work on 5-12V, so I would probably use a 12V power supply.
As a more general rule, if something can take a range of input voltages, always supply something on the higher end of the range. Running low-voltage DC through longer cables is a major pain, so going with the higher voltage means you're compensating for drop in the cable. If your 12V arrives as 10V that's fine, but if your 5V arrives as 3.5V it's less good.
This is also why many USB power supplies output 5.1 or even 5.2V, and why many switching regulators have cable drop compensation circuitry built in. Which the manufacturers of the Middle Kingdom then either ignore or copy the values from the data sheet, getting it wrong either way.