Motion Sensors sharing 5V supplies?

Hi. I have (had?) an Ademco Accord XpC from about 2001/2002. It stopped working, so I thought I'd give Konnected a shot. I'm in Ireland, so it's a UK-type system – and there's no wiring diagram anywhere on the system.

The system had 5 zones hooked up to the original board: 1x front-door open/close sensor, and 4x motion sensors. However, there are only 2x 5V Aux connections in total to power all 4x motion sensors (there was a 3rd Aux connection, but I figured out it was to drive the keypad).

I'm assuming that the Konnected board does't have enough power to drive 4x sensors from 2 wires. I say this because, while the sensors all do get some power from the 2x 5V connections, they're not being very good at detecting at range (they work at close range, like if I wave my hand directly in front of a sensor).

Has anyone seen a setup like this before, where multiple motion sensors are driven from a single 5V input? Could they be connected in series?

I was hoping for some help before I start ripping up carpets and tearing down sensors.  :)