Ant

... and have had it...
... and I have had it ...

But 2002 was far more than five years ago.

Some people will say that if you repeat the subject, you should have a comma before "and" but others ignore this old "rule."

What does "Ant" have to do with your question?

Not really, but "I bought my car in 2002, and I have had it for five years now" would have been correct in 2007.

I will do nothing with it. This question is from Grammar Workshop with unknown year of publishing (m.b. 2007?).

What do you mean when you say you will "do nothing with it"?

The tense was incorrect as a stand-alone sentence.

So, I don't know what to do with the sentence in Past tenses "I ___(buy) my car in 2002 and I ____ (have) it for five years now". I decided that it must has such view "I bought my car in 2002 and I had had it for five years now." Is that right?

This is a matter of logic rather than grammar. "I bought my car in 2002 and I have had it for five years now" is a perfectly grammatical sentence, but it doesn't make much sense in 2015.