With 5 special cards and 16 normal cards in the deck the following is true: 
The probability to finish on turn 21 or later is 23.8%
The probability to finish on turn 20 or later is 42.85%
The probability to finish on turn 19 or later is 57.89%
The probability to finish on turn 18 or later is 69.59%
The probability to finish on turn 17 or later is 78.53%
The probability to finish on turn 16 or later is 85.24%
The probability to finish on turn 15 or later is 90.16%
The probability to finish on turn 14 or later is 93.67%
The probability to finish on turn 13 or later is 96.1%
The probability to finish on turn 12 or later is 97.72%
The probability to finish on turn 11 or later is 98.76%
The probability to finish on turn 10 or later is 99.38%
The probability to finish on turn 9 or later is 99.72%
The probability to finish on turn 8 or later is 99.89%
The probability to finish on turn 7 or later is 99.97%
The probability to finish on turn 6 or later is 99.99%
The probability to finish on turn 5 or later is 100.0%