Is a divorce issued in anger not valid in Islamic law? And is it permissible for me to return to my wife after divorcing her five times without witnesses or a new marriage contract, knowing that we are currently living in stability and tranquility and have two children?

Divorce pronounced in a state of anger is valid unless the anger reaches a level that causes the person to lose discernment. Islam made it easy for a man by giving him two opportunities (the first and second pronouncements of divorce). You, however, made it difficult for yourself and destroyed your family through your haste and anger. You must separate from this woman immediately. If she completes her waiting period ('iddah), marries another man with the intention of marriage and not just to make her lawful for you (tahlil), and he consummates the marriage with her, and then he divorces her or dies, and she completes her 'iddah from him, then it is permissible for you to marry her.