Bruno's father is a Nazi commandant. Under orders from the Fuhrer ('Fury' to Bruno's nine year old ears), the whole family must move to Auschwitz ('Out-With' to Bruno) as Bruno's father has been selected to oversee operations at the death-camps there.
Bruno's father is used to being obeyed, both by his family as well as by soldiers under his command. For example, Bruno is never to enter his father's office for any reason; it is 'Out Of Bounds At All Times And No Exceptions.'
Bruno describes his father as a meticulous man. His personal appearance is impeccable and his voice authoritative; his uniform is pressed to perfection and his hair lacquered carefully. Bruno's father looks every inch the commandant that he is. He doesn't have to raise his voice even when he is giving an order. An example of his quiet confidence is displayed when he dismisses his soldiers with a well-placed joke.
Your suggestions and your encouragement are very much appreciated...Here we have a fresh beginning, but let that beginning start tomorrow. For now, I'd better help my family settle in or there will be as much trouble for me in here, as there is for them out there, you understand?
Although the soldiers laugh and march out mechanically, voicing their usual 'Heil, Hitler' on the way, this jovial manner betrays an intimidating menace. After all, the 'trouble' for the people out there is that many of them will die in gas chambers without promise of hope or mercy. The soldiers know that Bruno's father is the ranking official overseeing this mass operation; he definitely is a man to be obeyed.
Being that he is a military commander, Bruno's father is also not given to expressions of affection. Bruno tells us that he receives handshakes from his father, rather than the customary hugs he is used to receiving from his mother and grandmother.
Even though the commandant is a man who possesses iron control, he is not without compassion for his young son. When Bruno daringly knocks on his father's door at their new home, he is beckoned in by his father's booming voice. Bruno doesn't really like this new home in Auschwitz; the surroundings are gloomy, the soldiers unfriendly, and there is no one his age to play with.
Bruno's father listens sympathetically and even allows his son to express his frustrations. However, he will only tolerate questioning of his motives up to a point. He reminds Bruno that he (Bruno) must trust in his father as he himself had to trust Bruno's grandfather when he was young.
...I have listened to what you have to say, even though your youth and inexperience force you to phrase things in an insolent manner. But the moment has come when you will simply have to accept...
When Bruno asks about the people living in huts in the distance, Bruno's father tells him that those people are not considered humans at all. Here, in words of chilling inhumanity, Bruno's father betrays his sadistic side. He reiterates that he expects Bruno to accept his situation without further question. Interestingly, it appears that this is the way he himself accepts orders from the Fuhrer.
To summarize, Chapter 5 reveals Bruno's father as a staunch idealogue (one who is excessively devoted to a cause) who expects the same obsessive adherence to Nazi ideals without question.