Question

how many different visible lines are emitted during transition form 5th orbit to ground state in hydrogen emission spectrum

Answer 1

no. of lines = n(n-1) /2
here​ n = 5
No. of lines = 5(5-1)/2 =10 lines

Answer 2

(n₁+n₂)(n₁+n₂-1)/2 here n₁=1,n₂=5 
So, 6(6-1)/2=30/2=15.