How many numbers greater than 5000 can be formed with the digits 3,4,6,8,9 if a digit cannot occur more than once in a number?

We can split this into 2 cases:

4-digit numbers and 5-digit numbers

4-digit numbers:

it'll only be greater than 5000 if the first digit is 6, 8, or 9. The other 3 digits can be anything else, so there are a total of 3*4*3*2=72 4-digit numbers

5-digit numbers: all 5-digit numbers are greater than 5000, so there are a total of 5*4*3*2*1 = 120 5-digit numbers

the total is 72+120=192 numbers greater than 5000

With no upper limit on the numbers, an infinite number of them can be written.