Find the no. of visible lines when an electron returns from 5th orbit to ground state in H spectrum

First we find the total number of transitions. They are as follows.

(5,4),(5,3),(5,2),(5,1)………….(4) transitions

(4,3),(4,2),(4,1)…………………(3) "

(3,2),(3,1)…………………………(2). "

(2,1)…………………………………(1). "

Total number of transitions is =10.

Now, we know that lines of Balmer series in H- atom spectrum fall in visible region. The transitions TO n=2 level gives Balmer series. So,transitions (5,2),(4,2) and (3,2) give (3) visible spectral lines if initial level is n=5.