The correct answer is A.
The sentence “I have lived in Delhi since five years” means that the speaker has been living in Delhi for a period of five years that continues up to the present time.
The sentence “I have lived in Delhi for five years” could mean either that the speaker has been living in Delhi for a period of five years that continues up to the present time, or that the speaker lived in Delhi for a period of five years in the past but no longer lives there.
The sentence “I lived in Delhi five years ago” means that the speaker lived in Delhi at some point in the past five years but no longer lives there.
The sentence “I lived in Delhi for five years ago” is grammatically incorrect.