The degree of freedom of a molecule refers to the number of independent ways in which it can move. In the case of a diatomic gas, the molecule consists of two atoms that are bonded together.

Types of degrees of freedom:
1. Translational degrees of freedom: The molecule can move in three directions i.e., x, y, and z axis. Therefore, the total number of translational degrees of freedom is 3.

2. Rotational degrees of freedom: The molecule can rotate about its center of mass in two directions i.e., pitch and yaw. Therefore, the total number of rotational degrees of freedom is 2.

3. Vibrational degrees of freedom: The molecule can vibrate along the bond axis. In the case of a diatomic gas, there is only one bond, so there is only one vibrational degree of freedom.

Calculation of degree of freedom:
The total degree of freedom of a diatomic gas is the sum of its translational, rotational, and vibrational degrees of freedom.

Total degree of freedom = Translational degrees of freedom + Rotational degrees of freedom + Vibrational degrees of freedom

= 3 + 2 + 1

= 6

However, it is important to note that the vibrational degree of freedom is not always considered for an ideal gas because the energy required to excite the molecule's vibrational motion is much larger than the thermal energy of the gas. Therefore, for an ideal diatomic gas, the degree of freedom is taken as 5, which is the sum of translational and rotational degrees of freedom.

Hence, the correct answer is option C, which is 5.