Is a new marriage contract required if the intention to marry was absent in the first contract, and then this intention became present after five years of a formal marriage that was documented both Islamically and legally?

There is no such thing as a "white marriage." As soon as there is an offer and acceptance, the marriage takes place, even if one or both parties are joking. This is the view of the majority of jurists, based on the Prophet's (peace be upon him) saying: "There are three things which, whether done seriously or in jest, are taken seriously: marriage, divorce, and revocation [of divorce]." Therefore, there is no need to renew the contract.