The correct answer should be 216.
First we deal with the 4 digit numbers: [] [] [] []
As for the first digit, only 5, 7 ,8 and 9 can be used, as utilizing 3 will lead to the number being smaller than 4000 thus does not satisfy the condition of >4000.
In order to find out how many 4 digit numbers that are >4000, we use 4P1x4P1x3P1x2P1=96 numbers.
(We pick one number from 5,7,8,9 for 1st digit, and at the 2nd digit, 3 can now be used hence there will still be 4 numbers to pick on for the 2nd digit, we have used 2 numbers so far, thus the 3rd digit having 3 to pick from, the last digit having 2 numbers to pick from. That explains for the eqn above)
Now we move on to five digit numbers. It is fairly straight forward since all five digit numbers are >4000, thus we can just use 5P5=120
120+96=216

note that when dealing with situations where the ORDER does matter eg. numbers and letters, we use nPr instead of nCr

hope this helps!

This is not a GMAT type question ! Please post only GMAT type question.

I am definitely I proponent of calling out non-GMAT questions here, but I think this one is totally reasonable.

Hi - I think GMAT Sucker may have also meant the language or wording of the question is not clear or GMAT like.

So if repetition of the digits is NOT ALLOWED, then the explanation above is perfect, and nicely done.

But if the repetition of digits is allowed, (which is not specified in question above) then we have a different answer naturally.

Thanks
Kaps