Depends on counting. A 5 year old might be getting his first permanent molar, which would look like a third baby molar coming through, behind his 2 baby molars.
Highly unlikely. The tooth buds that will eventually form wisdom teeth usually do begin to form until around the age of nine or later. It is very possible what you are seeing is the early eruption of the first permanent molar. Even though they are referred to as the six year molars, they can show up earlier or later then six.
1st Permanent molar. Yes, this is her first permanent molar. These teeth are often called "six year molars" as they come in around the age of six, but some children do get them at age 5. They erupt behind the last baby tooth. A baby tooth does not come out when the 1st permanent molar comes in.
Yes and it is likely. Her permanent first molar if it is located just behind the "baby" tooth you have seen for the past 3 years. She is just about the correct age for the normal eruption of this adult tooth. Expect some soreness in the area while it is erupting.
Perfectly normal. Girls teeth earlier than boys, so 6 year molars often erupt at 5-6 for girls, 6-7 for boys. Your daughter currently has 2 baby molars in each quarter of her mouth that will eventually fall out and be replaced by permanent premolars. Behind the baby teeth erupt the 6year molars, the12 year molars, and as a late teen the wisdom teeth. See an orthodontist for eruption guidance.
1st permanent molar. Your son/daughter is getting his/her first permanent molar (sometimes called 6 year molars). This is perfectly normal.