If, where and how to talk about personal problems during master in PhD application
I suggest you say very little in your application materials. Nothing more than "My completion was delayed by medical/(or whatever) considerations, now resolved." 

Just that. If you get into a situation in which you need to say more, it will likely be with a small group and you can go into detail as you see best. 

They will have some valid concern that the old issues won't cause a problem in the future, so be prepared to address that. 

And who can say, even yourself, what contributed to the delay. Illness, family problems, lots of things can cause stress that reduce focus and make things harder. Don't make assumptions that you've done wrong, at least not in public.