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Always refer to the manual that comes with the model year of the car. The 2013 M5 Sedan owner's manual states on page 177 to use SAE0W-30 or SAE0W-40 or alternatively,
SAE5W-30 or SAE5W-40 with specifications ACEA A3/B4, API SK/CF or superior grade specification. Page 178 states "BMW recommends Castrol".
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