If the calender table indicates 4:45 a.m. as Ishraq till what
time can Fajr be prayed?
If what is published in the calendar conforms to what is actually observed in reality, then the answer to your question is what was narrated by Abu Huraira in the hadith of the Prophet (peace be upon him): "Whoever catches a raka'a of the morning prayer before the sun rises has caught the prayer" (i.e. on time) (Bukhari).
It must be noted, however, that praying the five daily congregational prayers in the mosque is wajib (compulsory) for men.