I thought I would share the process to fix that annoying broken "backrest claspe", the little M-colors emblem on the M5 front seats. It is so easy you really will wonder why you didn't do it sooner. You do not even need to remove the seat to replace it.
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The item you want for the front seats is 52101927000. It is called a "Claspe Backrest Front" by BMW, there are at least a few available, and they should cost $11-14 each...until inventory gets really low. You can get them from your usual OEM parts source but if they can't find them, ECS Tuning often has good luck finding NLA and almost NLA parts. Once you get the clasp, go to your local ACE Hardware or someplace that has a very good nuts and bolts selection. Big box lumber stores probably won't do. You need some push-in locking clips (like the kind that held wagon wheels on your/your kid's wagon) some small stainless washers and some RUBBER fender washers. The locking clips, of course, need to fit securely on the aluminum pins in the back of the clasp. Buy some extras because they bend very easily and once bent, won't work.
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Once you have all the parts, adjust the seat so it is as high as possible, grab a phillips head screwdriver and unscrew the two screws at the bottom corners of the seat back. You might want to put the headrest all the way up so you have a little more room to work inside the seat. The seat back secures with only those two screws and two clips that hook over the seat frame at the top. Loosen the bottom and pull the back straight up to remove it. Here is an image of the inside of the back so you can see where the screws and clips are located.
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Now you can get to your broken clasp and remove it. There is some cloth to protect the seat back and clasp from the headrest mechanism. Just move it out of the way. The posts are aluminum and will cut easily with a large pair of diagonal wire cutters. Here is a shot of the seat back. Note, my seat was out of the car but you do not have to remove it.
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Now, just push the clasp pins through the seat were the original holes were. Insert the rubber fender washer, then the stainless washer, then the locking clip. I used a small socket to push the clip onto the pin. Do not push the first side too tight onto the seat. Leave it a little loose and then alternate tightening until the clasp sits where you want it to on the front. Here is an image of the fender washer, washer and locking clip inserted onto the clasp pin.

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When you are happy with the way it looks, use some wire cutters and clip off the pin leaving at least a half inch on the seat. One of the seats on my other M5 had the clasps installed with the pins bent inward and the pressure of sitting on the seat eventually warped and broke the clasp. Make sure what is left does not interfere with the headrest mechanism.

Move all of the protective cloth back into place in front of the headrest mechanism and replace the seat back. All done!