Key Points:
- The stone is thrown vertically upwards with an initial speed of 5 m/s.
- The acceleration due to Earth's attraction, also known as the acceleration due to gravity (g), is 9.8 m/s².
- We need to calculate the maximum height reached by the stone before it returns back to the Earth.

Analysis:
To solve this problem, we can use the equations of motion to determine the maximum height reached by the stone.

Step 1: Identify the Given and Required Values
Given:
- Initial velocity (u) = 5 m/s (upwards)
- Acceleration due to gravity (g) = 9.8 m/s² (downwards)

Required:
- Maximum height reached by the stone (h)

Step 2: Determine the Time of Flight
The stone will reach its maximum height when its final velocity becomes zero. The final velocity (v) can be determined using the equation:

v = u + gt

where:
v = final velocity (0 m/s at maximum height)
u = initial velocity (5 m/s upwards)
g = acceleration due to gravity (9.8 m/s² downwards)
t = time of flight

Rearranging the equation, we get:

t = (v - u) / g

Substituting the given values, we have:

t = (0 - 5) / (-9.8) = 0.51 s

Step 3: Calculate the Maximum Height
The maximum height reached by the stone can be determined using the equation:

h = u * t + (1/2) * g * t²

where:
h = maximum height
u = initial velocity (5 m/s upwards)
g = acceleration due to gravity (9.8 m/s² downwards)
t = time of flight (0.51 s)

Substituting the given values, we have:

h = 5 * 0.51 + (1/2) * 9.8 * (0.51)²
= 2.55 + 1.26
= 3.81 m

Answer:
The stone rises to a height of approximately 3.81 meters before returning back to the Earth.