39089

There are 16 ways of going down the 5 stairs.
(5)
(3,2)
(2,3)
(1,1,1,1,1)
(4,1)
(1,4)
(1,2,2)
(2,1,2)
(2,2,1)
(1,2,1,1)
(2,1,1,1)
(1,1,1,2)
(1,1,2,1)
(3,1,1)
(1,3,1)
(1,1,3)
In order to know this, i drew a 5 block stairs. Made a chart of all possibilities numbers added to 5.

For 4 stairs, there are 8 ways.
(4)
(1,1,1,1)
(2,2)
(3,1)
(1,3)
(2,1,1)
(1,2,1)
(1,1,2)