Biblical Commentary by Clarke gives us some reasons of why Joseph might have chosen only 5. Two of them are:
- Joseph took five of the meanest-looking of his brothers fearing that Pharaoh would detain them for his service, whereby their religion and morals might be corrupted.
- Joseph took five of the best made and finest-looking of his brethren and presented them before Pharaoh, wishing to impress his mind with a favorable opinion of the family which he had just now brought into Egypt, and to do himself honor.
My personal opinion is that as Joseph he wanted his brothers to stay in a fertile land in Egypt. He asked them to state to the Pharaoh that their job is to tend livestock. Livestocks are naturally kept in a fertile land during a famine. But the problem is as Joseph himself states, in Gen 46:34, that shepherds are detestable to the Egyptians. So he took only half of his fathers sons so that not to make the Pharaoh detest them.
Or Joseph might have been afraid that if he brought forth all of his 11 brothers at once, the Pharaoh might find them intimidating and Joseph might lose his favor.
In the next verses we also see that Jacob visits him separately. Probably that could be a royal custom to meet a Pharaoh in small groups.
In his commentary Clarke also continues to say that in Judges 18:2, the word extremity (מקצה miktseh - the word which also appears in Joseph's selection of his brothers) may be understood as implying dignity, valor, excellence, and per-eminence. It is probable they might have followed what Joseph did here because the mission was important.
Here is the full text of Clarke's Commentary on the Bible for Genesis 47:3.