You may have already tried this but I wanted to reach out just in case, there is a technique for leveling the Taz 5’s bed. Leveling the bed on a TAZ can be a little tricky until you get the hang of it. The most common issue new customers run into is making too large of adjustments to the corner pieces. In order to have a good starting point, please reset your bed. You are going to want to compress the corner springs to 3/4ths their maximum position. The easiest way to do this is to place your finger underneath the aluminum build plate, and tighten all for corners until the screws are sticking out to the same length. This gives a base starting point that allows for tightening and loosening on all 4 corners.
Once the bed is reset we need to set the initial Z height before making any corner adjustments. Measure the distance from the aluminum plate to the lower horizontal smooth rod of the X axis on both the right and left hand side. This should be equidistant. If an adjustment is required, turn off your printer and manually turn one of the threaded rods up or down to make the left and right hand side equal. Using a business card between the glass plate and the nozzle, home your printer. When it has finished moving, you should feel a slight tension on the card from the nozzle and the bed. If this pressure is not present, or is more than slight you will need to adjust your Z axis thumb screw and re-home. Once this is set in the home position, we can test the other three corners.
Turn off your printer or disable your stepper motors to allow manual movement of the bed and tool head. Move the tool head and the bed to test all 4 corners approximately 1 inch in from the sides. You should feel the same slight tension on the card on all four spots. If needed, adjust the bed corners to achieve this. The bed corners work much in the same way as replacing a car tire. You will want to make small adjustments as changing one corner will affect the other three. The business card it just a quick set in order to get your bed calibration print to stick. Fine adjustments will be made after the bed calibration print to achieve the proper height as highlighted in step 5 of your quick start guide.
Here is a helpful link to the online instructions on bed leveling: https://www.lulzbot.com/support/taz-bed-leveling
Here is another helpful link to that same procedure but in video form: https://www.youtube.com/watch?v=EdB8jbXFfns