The number of red flowers is twice as many as orange so 2 * 10 orange = <<2*10=20>>20 red flowers
The number of yellow flowers is 5 less than red so 20 red - 5 = <<20-5=15>>15 yellow flowers
The number of red, orange and yellow flowers is 20 red + 10 orange + 15 yellow = <<20+10+15=45>>45 flowers
The number of pink and purple flowers total is 105 flowers total - 45 flowers that are not pink or purple = <<105-45=60>>60 flowers
The number of pink and purple flowers each is 60 flowers / 2 = <<60/2=30>>30 flowers each
#### 30