X5 e53 2003 failed not on front to rear brake pipes, these were replaced issue appeared with front brakes fine after bleeding rear brakes would not bleed up. Rear calliper bleed nipple seize, so replace with new calliper, still issue. Replace brake master cylinder, still issue. Sent abs pump off to be reconditioned, come back from testing stating beyond repair. Got secondhand unit exactly same part number, with warranty, still not bleeding rear brakes. Please anyone out there with possible ideas that would help me? Many thanks in advance!

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Morning David

Welcome to the Forum

First a couple of questions (1) Do you have access to a Good BMW Diagnostic program (ISTA/INPA, iCarsoft, Foxwell,or similar) and a vacuum bleeding kit (2) Have you read the brake bleeding process on INPA/ISTA the ABS pump needs activating to clear possible air locks

Not trying to teach Granny here but 😁

When bleeding brakes changing Brake fluid I start at the wheel furthest from the Master cylinder, Fill the Master cylinder and pump the pedal to start the fluid moving, either take your time a few pumps and check the fluid level or have an assistant to keep it topped up. After a bit you should feel pressure, now crack the bleed nipple on the wheel furthest from the Master cylinder air should be expelled If you have a Vacuum kit it will pull through the fluid if not you and your assistant will need to follow the old method of pedal down close bleed nipple pedal up check fluid level pedal down bleed nipple cracked air/fluid expelled bleed nipple closed repeat until just clear fluid is coming through before moving to the next cylinder (always furthest away from the Master cylinder) So Near side rear, Off side rear, Nearside front , Off side front. Once all 4 calipers have been Bled the ABS pump needs activating to finalise the process.

If you still have a soft pedal an old trick is pump the pedal until hard cut a piece of wood to fit between the brake pedal and drivers seat then wedge the wood there to keep the pressure up (I have used the electric seat to adjust). It needs to be left for a couple of hours even overnight then re-bleed, had a neighbours 5 series that needed this done 3 time really stubborn 🤣

Hope this helps

Dave