We’re being asked to determine the number of orbitals for n = 5 and l = 0-5 (n instead of n-1).
Recall that the quantum numbers that define an electron are:
• Principal Quantum Number (n): deals with the size and energy of the atomic orbital.
The possible values for n are 1 to ∞.
• Angular Momentum Quantum Number (l): deals with the shape of the atomic orbital.
The possible values for l are 0 to (n – 1).
• Magnetic Quantum Number (ml): deals with the orientation of the atomic orbital in 3D space.
The possible values for ml is the range of l: –l to +l.