Divide thy problems into two problems.

1)You get 1,2,3,4,5

2)You get 2,3,4,5,6

Without loss of generality the probability is the same in both problems.

If you are trying to get: 1,2,3,4,5.

So the probablity in that order is,

Multipled by the number of ways you can get these arrangements which is

Thus,

Now the probablity of: 2,3,4,5,6

Is too

Thus, the total probability is,