The height of a tree is the length of the longest root-to-leaf path in it. The maximum and minimum number of nodes in a binary tree of height 5 are

Given that the height of the tree $h = 5$, where height is defined as the length of the longest root-to-leaf path (number of edges from root to leaf):

1. Maximum number of nodes: A binary tree attains the maximum number of nodes when it is a full (complete) binary tree where every level is fully populated.

   $$N_{\max} = 2^{h+1} - 1 = 2^{5+1} - 1 = 2^6 - 1 = 64 - 1 = 63$$

2. Minimum number of nodes: A binary tree attains the minimum number of nodes when it is skewed (each level has exactly 1 node).

   $$N_{\min} = h + 1 = 5 + 1 = 6$$

Thus, the maximum and minimum number of nodes are 63 and 6, respectively, which corresponds to option (A).