It is permissible to pray your night prayer in the format you stated.

If sunrise is at 5:19, praying fajr at 5:00 is too late and you have to pray it earlier.

We are in summer seison now and the praying times for isha dan subuh prayers are so close. For example, isha is at 23.50, and subuh prayer is at 03.04 am. It is difficult to do the tahajjud praying, since I have known (if correct) that shalat tahajud should be done after ones has slept, after isha prayer. Is it ok if I just do the shalat isha, then 2 raka’at shalat sunnah, then shalat tahajud, followed with witir ? Aside from that, I have some difficulties to do shalat subuh, so mostly I do it around 05.00 am, is it also ok ? Fajr is at 05:19.