If a $\mathbf{2 7}$ feet tall tree casts a $\mathbf{1 5}$ feet shadow, what is the height of a tree if its shadow is $\mathbf{5}$ feet long?

Step 1 ：Given a 27 feet tall tree casts a 15 feet shadow, we are asked to find the height of a tree if its shadow is 5 feet long.

Step 2 ：This is a problem of similar triangles. The ratio of the height of the tree to the length of the shadow is constant. So, we can set up a proportion to solve for the unknown height of the second tree.

Step 3 ：Let's denote the height of the second tree as \(h\). The proportion can be set up as follows: \(\frac{27}{15} = \frac{h}{5}\)

Step 4 ：We can solve this equation for \(h\).

Step 5 ：\(h = \frac{27}{15} * 5 = 9.0\)

Step 6 ：Final Answer: The height of the tree that casts a 5 feet shadow is \(\boxed{9}\) feet.