Until what time can the Fajr and Asr Salaah be read?

Assalamu alaikum. Respected Mufti Sahab, I want to ask
In case of Asar namaz, suppose the of Gurub of Aftab is at 5.45pm, so if someone arrived late due to some reason so can he read the namaz till say 5.40 or last till 5.45pm so that the namaz does not become Qadha. Can one do like this or not. Some say the Asar namaz has to be read 10 minutes before Gurube Aftaab. So in this case will one read it or leave it if the time has crossed 5.35.pm and then make the namaz Qadha and read it after Magrib the qadha though there was time of ten minutes before the azaan of magrib. What is correct and what should one do in these cases. Jazzak Allah