The height of a tree is the length of the longest root-to-leaf path in it. The…

Answer: Maximum = 63 nodes; Minimum = 6 nodes.

Reasoning (assuming height is the number of edges on the longest root-to-leaf path):

• Maximum nodes: A perfect binary tree of height h has h+1 levels, and the total number of nodes is 2^{h+1} - 1. For h = 5, this gives 2^{6} - 1 = 64 - 1 = 63.

• Minimum nodes: The minimum occurs in a skewed tree with exactly one node on each of the h+1 levels, so the minimum number is h+1. For h = 5, this is 5 + 1 = 6.

Note: If a different definition of height is used (for example, counting nodes instead of edges along the longest path), formulas would shift accordingly. Under the edge-count definition used here, the correct pair is 63 and 6.