If the couple haven't been married and they lived together so long, now they are separated. If either one of them want to get married, do they have to file divorce first? The reason I asked.. because one of my friends told me that it was happened to one of her friend.

Texas does have common law or informal marriage

It is not only the living together, but also have agreed to be married and publicly represented themselves as married.

So you could live together for years and not be common law, it is not the number of years, it is what the couple does when living together

Common Law Marriage in Texas

If the couple live together for about 5 years. They only filed tax together as married couple for one time and bought car insurance together as married couple.do they still consider as common marriage.

Well of course besides being tax fraud, ( another issue unless they were common law)

But yes, it appears they represented theirself as married, because of this.

So they should do a divorce though the court ( there is no common law divorce) before they do anything else