When should I perform congregational prayer fully if someone is praying next to me, knowing that I usually do not vocalize the takbir or recitation when a five-year-old child prays next to me, and I pray as if I am praying alone?

A child who has not reached the age of discernment is not held accountable for their actions, nor are their actions recorded. They do not have a prescribed prayer, and their imamate in prayer is not legislated. If a boy reaches the age of discernment (seven years or the age at which he understands distinctions), his prayer is valid, and a congregational prayer can be formed with him as an imam. It is permissible for a solitary worshiper to change their intention to lead the prayer if a discerning boy stands beside them. Congregational prayer is obligatory for adult men who have no valid excuse.