The lowest value of n that allows the g orbital to exist is 5.

Explanation:
The g orbital is one of the five d orbitals. It has a complex shape and can hold a maximum of 10 electrons. The d orbitals exist in the energy levels beyond the s and p orbitals.

Energy Levels and Subshells:
- The energy levels in an atom are represented by the principal quantum number (n).
- The value of n determines the size and energy of the orbital.
- The subshells, which are further divided into orbitals, are represented by the azimuthal quantum number (l).
- The value of l determines the shape of the orbital.

Order of Filling Orbitals:
The order of filling orbitals is determined by the Aufbau principle, which states that electrons fill the lowest energy level orbitals first before moving to higher energy level orbitals.

Order of Filling Orbitals:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p...

Explanation:
1. The s orbitals (spherical) are filled first, starting with the 1s orbital, followed by 2s, 3s, 4s, and so on.
2. The p orbitals (dumbbell-shaped) are filled after the s orbitals, starting with the 2p orbital, followed by 3p, 4p, and so on.
3. The d orbitals (complex shapes) are filled after the p orbitals, starting with the 3d orbital, followed by 4d, 5d, and so on.
4. The f orbitals (even more complex shapes) are filled after the d orbitals, starting with the 4f orbital, followed by 5f, and so on.

The g Orbital:
- The g orbital is the fifth orbital in the d subshell.
- It is filled after the 4s, 3d, and 4p orbitals.
- Therefore, the lowest value of n that allows the g orbital to exist is 5.

Answer:
The correct answer is option 'D' (5).