The Adhan for Fajr is almost to the end of time, but dawn is half an hour before

Prayer timetable says that dawn is at 3:53am, and the sun rises at 5:45am. The Adhan for Fajr is very close to 5:45, something like 20minutes before. My question is, if I am going to fast(Dhul Hijja) I can eat until dawn, can I pray Fajr before the Adhan around 4? Why is Adhan so late, or is it the timetable that is making the problem? If it is, if dawn is later than it is written, why does it say that it is that early and people can't eat anymore from that early time?