The time for Fajr (first prayer of the day in early morning) is till the sunrise. So you have to check exact time for sunrise in your area, and pray before it, but it is highly recommended to pray at first time.
Proven from this hadith:
It was narrated from Abdullah bin Amr (RA) that the Prophet (PBUH)
said, “The time for Zuhr is so long as Asr has not come. The time for
Asr is so long as the sun has not turned yellow. The time for Maghrib
is so long as the twilight has not disappeared. The time for Isha is
so long as half of the night has not passed. The time for Fajr is so
long as the sun has not risen.” (Hadith No. 1386 (612), Book of
Masjids & Places of Prayer, Sahih Muslim, Vol. 2).
Also, in case you kept sleeping,then according to one hadith (i dont have it with me now) the time for prayer is, when you wake up (means, as soon as you wake up, and the time of prayer is gone,then pray as soon as you wake up.
Hope that answers the question