Add apple cider vinegar, mustard, sugar, salt and pepper to a large bowl (your serving/storage bowl) and whisk. Add in mayo and mix well until combined.
Using a knife or a food processor, finely chop the cabbage and carrots.
Add the cabbage, carrots, and raisins (if desired) to the dressing and mix until everything is coated.
Store in the fridge up to 5 days.