The number of degrees of freedom refers to the number of independent motions or variables that a mechanism can have. In this case, we are considering a five-link plane mechanism with five revolute pairs. Let's break down the mechanism and analyze its degrees of freedom.

The five-link plane mechanism consists of five links connected by revolute pairs. A revolute pair allows for rotation between two links.

1. Identifying the Links:
- Link 1: The fixed base of the mechanism.
- Link 2: Connected to the base and can rotate around its revolute pair with link 1.
- Link 3: Connected to link 2 and can rotate around its revolute pair with link 2.
- Link 4: Connected to link 3 and can rotate around its revolute pair with link 3.
- Link 5: Connected to link 4 and can rotate around its revolute pair with link 4.

2. Identifying the Joints:
- Joint 1: Located between link 1 and link 2, allowing rotation.
- Joint 2: Located between link 2 and link 3, allowing rotation.
- Joint 3: Located between link 3 and link 4, allowing rotation.
- Joint 4: Located between link 4 and link 5, allowing rotation.
- Joint 5: Located between link 5 and the end effector, allowing rotation.

3. Analyzing the Degrees of Freedom:
To determine the degrees of freedom, we count the number of independent motions or variables. In a revolute pair, there is one degree of freedom, which is the rotational motion. Since all the joints in this mechanism are revolute pairs, the number of degrees of freedom is equal to the number of joints, which is 5.

Therefore, the correct answer is C: 2 degrees of freedom.

Just apply kazboch equation F = 3(n-1) - 2j - h here n=5 , j=5, h=0 you will get F = 2 !