Is it permissible for children (four daughters and a boy, aged between 6 and 10 years) to massage their father's back and limbs? And does the ruling change after they reach puberty?

It is understood from the question that the man enjoys having his limbs rubbed for normal relief from fatigue, without lust or pleasure in the person rubbing him. Therefore, there is no harm in his sons and daughters—whether adults or not—rubbing the aforementioned limbs, except for the area between the navel and the knee. This area is awrah (private parts) and must be covered, but it is permissible for them to look at other areas.

However, if the intent of the pleasure is lust in the person rubbing him, then it is forbidden and a gateway to great evil. Even though the first case is permissible, it is not recommended to make a habit of it, especially with adults, as it may lead to breaking the father's modesty and awe before his children, and as a preventative measure against corruption.