To find the length of the tree's shadow using the information given, we can use the concept of similar triangles, since the tree and the fence post, along with their respective shadows, form similar triangles.
Let \( h_1 = 5 \) feet (height of the fence post), \( s_1 = 2 \) feet (length of the fence post's shadow), \( h_2 = 24 \) feet (height of the tree), and \( s_2 \) be the length of the tree's shadow that we want to find.
Using the ratio of the heights to the lengths of their shadows, we can set up the following proportion:
\[ \frac{h_1}{s_1} = \frac{h_2}{s_2} \]
Substituting in the known values:
\[ \frac{5}{2} = \frac{24}{s_2} \]
Now, we can cross-multiply to solve for \( s_2 \):
\[ 5 \cdot s_2 = 2 \cdot 24 \]
\[ 5 \cdot s_2 = 48 \]
Now, divide both sides by 5 to find \( s_2 \):
\[ s_2 = \frac{48}{5} = 9.6 \text{ feet} \]
Therefore, the length of the tree's shadow is \( \boxed{9.6} \) feet.