Answer
See explanation
Work Step by Step
All possible sets of four quantum numbers are
$(5,2,2,+1/2)$
$(5,2,2,-1/2)$
$(5,2,1,+1/2)$
$(5,2,1,-1/2)$
$(5,2,0,+1/2)$
$(5,2,0,-1/2)$
$(5,2,-1,+1/2)$
$(5,2,-1,-1/2)$
$(5,2,-2,+1/2)$
$(5,2,-2,-1/2)$