Do the same orbitals with a higher principal quantum number have a higher energy level than those with a lower principal quantum number.
As the principal quantum number of an orbital increases, the electron occupying the orbital moves farther away from the nucleus and the radius of its orbit increases. This requires the electron to have a higher energy level.
This is true for any two orbitals with differing principal quantum number. For instance electrons in the 1s orbital are at a lower energy level than electrons in the 2s orbital.
This is the reason why orbitals are always filled starting from those with a lower principal quantum number. The order in which electrons occupy orbitals is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p...