Check statement (A): Principal quantum number $n$
The principal quantum number can take positive integer values: n = 1,2,3,05 So, (A) is correct.

Check statement (B): Azimuthal quantum number $l$
For a given principal quantum number $n$, the allowed values of $l$ are: $l = 0,1,2,\dots,(n-1)$ But the statement says: $l = 0,1,2,\dots,n$ which is incorrect.
So, (B) is wrong.

Check statement (C): Magnetic quantum number $m_l$
For a given $l$, the magnetic quantum number can take values: $m_l = -l, -(l-1), \dots, 0, \dots, +(l-1), +l$ Total number of values: $2l+1$ So, (C) is correct.

Check statement (D): Spin quantum number
The two possible spin orientations of an electron are: $m_s = +\frac{1}{2},\,-\frac{1}{2}$ So, (D) is correct.

Check statement (E): Number of orbitals for $l=5$
For a given $l$, number of orbitals is: $2l+1$ For $l=5$: $2(5)+1 = 11$ not $9$.
So, (E) is wrong.

Correct set of statements
Correct statements are: $(A), (C), (D)$

Match with options
This corresponds to Option C.

Comparison with stored answer
Stored correct answer = C
Derived answer = C
Hence, they agree.