5:12 Does this mean that Christians cannot take an oath and swear to tell the truth even in a court of law?

Yes (CP Mt 5:33-37). Christians should not have to take an oath to attest to their truthfulness anywhere.

The Christian demand is for absolute faithfulness and truthfulness in all speech, and Christians must never play word games, exaggerate, or speak anything other than the absolute truth at all times.

For Christians not to observe this demand will bring God's condemnation upon them (CP Mt 12:36-37).