@CBUC,
Your probabilities for random guessing are wrong.
first attempt: 1/5
second attempt: 4/5 * 1/4 = 1/5
third attempt: 4/5 * 3/4 * 1/3 = 1/5
fourth attempt: 4/5 * 3/4 * 2/3 * 1/2 = 1/5
fifth attempt: 4/5 * 3/4 * 2/3 * 1/2 * 1 = 1/5
The expected number of attempts is:
1/5 * 1 + 1/5 * 2 + 1/5 * 3 + 1/5 * 4 + 1/5 * 5 = 3