The probability of getting a distinct number from the next box is now 4/5.
No. of additional box to get the second number = 1/(4/5) = 5/4.
(One can show that the expected value for the number of independent trials to get the first success is 1/p.)
The probability of getting a distinct number from the next box is now 3/5.
No. of additional box to get the third number = 1/(3/5) = 5/3.
The probability of getting a distinct number from the next box is now 2/5.
No. of additional box to get the third number = 1/(2/5) = 5/2.
The probability of getting a distinct number from the next box is now 1/5.
No. of additional box to get the third number = 1/(1/5) = 5.