Nope! All E39 M5s(1998-2003) are equipped with a Getrag Type D six-speed manual transmission with the following gearing ratios:
4.23(1), 2.54(2), 1.62(3), 1.23(4), 1.00(5), 0.83(6)
It is the same transmission used in the E39 540i but some changes were made to cope with the extra power the S62 engine produced. A reinforced clutch, rear differential utilizing a shorter 3.15:1 ratio and a limited slip differential with 25% maximum locking.
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