Is this a excuse for recovering prayer?

[Nitro Zeus]

Today, Dawn prayer started at 4:53AM, I woke up at 4:40AM so that I will have time to make ablution, but I have waited for couple of seconds so that I can officially wake up, but by mistake when I closed my eyes just for few seconds only(because I was so sleepy), then it happened that I slept all the way till Dawn prayer is over.

Do I have to recover the lost prayer? Will I still be sinful if I recover it?

[MazharShafiq]

yes you must have to recover your lost prayer .

[Nitro Zeus]

yes you must have to recover your lost prayer .

One more question. Today I've been on run from doctors to doctors and I spend hours there and also I went to gymnastics and I have missed all prayers, except Maghrib, and I went very late a home and I have recovered them in right order because I had no choice but to delay them. I had actually, a very busy day. And by mistake after I finised from recovering all prayers, I found on phone that the the time is over for Maghrib and Isha entered, and I started to think that I have finished few minutes after the time is over. Is this also a valid excuse for recovering prayers? Are my prayers valid if I did by mistake prayed few minutes after time is over? Because, it happened today this to me. And also, it wasnt in my hand this, I had to go to a female Christian psychologist because my mom wanted me to be assigned and she assigned me there. And I went also for eye and heart analyses I think, and we waited there for 1-2 hours for results. So, it wasnt in my choice.