The Problem:
A tree is broken at a height of 5 m from the ground, and its top touches the ground at a distance of 12 m from the base of the tree. We need to find the original height of the tree.

Solution:
To solve this problem, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Step 1: Identify the given information:
- The tree is broken at a height of 5 m from the ground.
- The top of the tree touches the ground at a distance of 12 m from the base.

Step 2: Visualize the problem:
To better understand the problem, let's visualize it. Draw a right-angled triangle with the broken tree forming the vertical side, the distance from the base to the top forming the hypotenuse, and the distance from the top to the ground forming the horizontal side.

Step 3: Label the triangle:
Label the vertical side as 'a', the horizontal side as 'b', and the hypotenuse as 'c'.

Step 4: Apply the Pythagorean Theorem:
According to the Pythagorean Theorem, we have the equation:
a^2 + b^2 = c^2

In this case, the vertical side 'a' is the height of the tree above the broken part (original height - 5 m), the horizontal side 'b' is the distance from the top to the ground (12 m), and the hypotenuse 'c' is the distance from the base to the top of the tree.

So, we can write the equation as:
(original height - 5)^2 + 12^2 = c^2

Step 5: Solve the equation:
Expand the equation and simplify it:
(original height - 5)^2 + 12^2 = c^2
(original height - 5)(original height - 5) + 144 = c^2
(original height^2 - 10original height + 25) + 144 = c^2
original height^2 - 10original height + 169 = c^2

Step 6: Find the original height:
To find the original height, we need to solve the equation. However, we need one more piece of information to solve it.