Installing ZMOD revealed a problem with my FlashForge Adventurer 5M which was either caused at the factory, during shipment (but the box is clean and shows no signs of mishandling) or my printer was a return that wasn't checked over before it was sent out again. This caused me to be unable to level the bed until I fixed it. The problem revealed itself as a "No Trigger on Probe After Full Movement" error during bed leveling.
I could actually hear the belt skipping teeth when ZMOD's center-probing load cell test occurred, though I didn't know what was happening at the time and it didn't give any error. Looking at the tensioner, it appears that the screws have been adjusted badly before, because they were overtightened. I might put a drop of nail polish at the head of the tensioning screw to stop this from loosening up again, which is probably what happened as there's no locking on this screw - which is a fundamentally sloppy design as there is not enough pressure on the threads to keep it in place without that.
I got the fix from this video, but you do not need a video to understand the fix. In fact a simple explanation is a lot quicker, though if you're a very visual person you might want to watch it. You simply flip your printer onto either the left or right side, loosen the two screws holding the belt tensioner in place (2.5mm hex) and then the screw with the spring on it (3.0mm hex.) Then while pushing the tensioner towards the back of the printer to create belt slack, turn all of the bed height screws counterclockwise (far side of the screw "to the left" when you're looking down from the top) until the bed hits the bottom. Now tighten things back up and run bed leveling. If you did it right and the printer is working correctly, you should now be able to level the bed.