Maximum possible height is found by using as less number of nodes for a given height as possible..But at the same time we have to preserve the AVL property..
So we have the recurrence :
H(n) = H(n-1) + H(n-2) + 1 where H(n) indicates minimum no of nodes in a AVL tree of height n..
The base cases are : H(0) = 1
H(1) = 2
So H(2) = 4
H(3) = 7
H(4) = 12
H(5) = 20..
As we are to able to have 20 nodes within height 5,
Hence , maximum height of an AVL tree possible with 20 nodes = 5