What can a divorced man do, who has a five-year-old son and wishes to marry, but his parents refuse out of fear for the son, and threaten to cut ties with him, while he fears falling into prohibitions and does not wish to disobey his parents?

If it is possible to reconcile with the former wife, that is best. Otherwise, he may marry another, and his parents have no right to prevent him from doing so. Marriage is encouraged in Islamic law and may even be obligatory. Fear that the new wife might mistreat the son is not a valid reason for prevention. The custody of the son belongs to his mother, then it transfers to whoever has more right to custody. Obedience to parents is not obligatory in all circumstances; rather, it is obligatory in matters that benefit them and do not harm the child. It is preferable to try and convince the parents, but if they do not agree, he should get married.