Your original sentence is awkward. It would make more sense to say something like "He bought his new car in 2015" or "He has been driving his new car since 2015."
These would all be correct:
"When did he buy his new car?" ("He bought his new car in 2015" or "He bought his new car five years ago" would make sense as answers.)
"How many years ago did he buy his new car?" ("He bought his car five years ago" would make sense as an answer.)
"How many years has it been since he bought his new car?" ("It's been five years since he bought his new car" or "He bought his new car five years ago" would make sense as an answer.)
"How long has he been driving his new car?" ("He has been driving his new car since 2015" and "He has been driving his new car for five years" would make sense as answers.)