Let's analyze and solve the problem in the image.

Problem Analysis:

• The block is at rest.
• Given:
  • Mass of the block ($m$) = 5 kg
  • Gravitational acceleration ($g$) = 10 m/s$^2$
  • Applied horizontal force ($F$) = 80 N
• The force of friction needs to be determined.

Since the block is at rest, the net force acting on it is zero. This implies that the frictional force balances the horizontal force applied to keep the block stationary.

Step-by-Step Solution:

1. Calculate the weight of the block: $W = m \cdot g = 5 \cdot 10 = 50 \, \text{N}$

   This is the force the wall must counter to prevent the block from sliding vertically. Hence, this weight is counteracted by the frictional force between the block and the wall.

2. Determine the frictional force: Since the block is stationary, the frictional force must equal the weight of the block: $f_{\text{friction}} = W = 50 \, \text{N}$

3. Final Answer: The force of friction acting on the block is 50 N.

Thus, the correct option is: $\boxed{\text{e) 50 N}}$

Would you like further clarification or details? Below are some related questions to expand on this topic:

1. How is static friction calculated when the coefficient of friction is given?
2. What would happen if the horizontal force $F$ were less than the weight of the block?
3. How would the frictional force change if the mass of the block increased?
4. What is the difference between static and kinetic friction in this scenario?
5. How would the answer change if the wall were smooth (frictionless)?

Tip:

When dealing with forces in equilibrium, always balance vertical and horizontal forces separately to simplify the problem.