39102

To find all the possibilities, I assumed that you can go down 1,2,3,4,5 steps. So all the possibilities are:

(5)
(4,1)
(3,2)
(3,1,1)
(2,3)
(2,2,1)
(2,1,2)
(2,1,1,1)
(1,4)
(1,3,1)
(1,1,3)
(1,2,2)
(1,2,1,1)
(1,1,2,1)
(1,1,1,2)
(1,1,1,1,1)
There are 16 ways in total.

If you can only go 1 and 2 steps, then there are 8 ways.
If you can 1,2,3,4 steps, then there are 14 ways.

The quickest way to find all the possibilities is to draw a diagram and write all the numbers in order to find all the ways. To make sure if you got all of the possibilities, double check it.

The size of the staircase doesn't affect the number of ways unless you can't go down 3-5 steps.