All the practices of Submission (Islam) originated from Abraham. This includes the five daily Contact Prayers (Salat). A careful analysis of the Quran confirms the five Contact Prayer (Salat) times based on the following verses:
Sura 24 verse 58 references two of the Salat times by name; that of the Dawn Contact Prayer (Salat Al-Fajr) and the Night Contact Prayer (Salat Al-Isha).
24:58 O you who believe, permission must be requested by your servants and the children who have not attained puberty (before entering your rooms). This is to be done in three instances—before the Dawn Prayer, at noon when you change your clothes to rest, and after the Night Prayer. These are three private times for you. At other times, it is not wrong for you or them to mingle with one another. GOD thus clarifies the revelations for you. GOD is Omniscient, Most Wise.
According to the Quran, the day starts from sunrise and ends at sunset (2:187). Therefore, from 11:114 we see references to the Dawn Contact Prayer, which occurs before sunrise at one end of the day, the Sunset Contact Prayer (Salat Al-Magrib), which occurs at the other end of the day, along with the Night Contact Prayer.
11:114 You shall observe the Contact Prayers (Salat) at both ends of the day, and during the night. The righteous works wipe out the evil works. This is a reminder for those who would take heed.
In 17:78, we see reference to the Noon Salat (Salat Al-Zuhr), which occurs after the sun declines from its highest point at noon as it heads towards night.
17:78 You shall observe the Contact Prayer (Salat) when the sun declines from its highest point at noon, as it moves towards sunset. You shall also observe (the recitation of) the Quran at dawn. (Reciting) the Quran at dawn is witnessed.
So far we have references to four of the five Salat times mentioned: Dawn, Noon, Sunset, and Night. 2:238 informs us that between these four prayers there is one last middle prayer. This would correspond to the Afternoon Prayer (Salat Al-Asr), as this would be the middle of the Dawn and Noon Salat on one side, and the Sunset and Night Salat on the other.
2:238 You shall consistently observe the Contact Prayers, especially the middle prayer, and devote yourselves totally to GOD.
In addition, to the Salat, God informs us that we should glorify God throughout the night and day, but this is in addition to the Salat. See also: 40:55, 52:48, 50:39, 3:41, 76:25-26, and 4:103.
20:130 Therefore, be patient in the face of their utterances, and praise and glorify your Lord before sunrise and before sunset. And during the night glorify Him, as well as at both ends of the day, that you may be happy.
3:41 He said, “My Lord, give me a sign.” He said, “Your sign is that you will not speak to the people for three days, except through signals. Commemorate your Lord frequently; and meditate (glorify) night and day.”
4:103 Once you complete your Contact Prayer (Salat), you shall remember GOD while standing, sitting, or lying down. Once the war is over, you shall observe the Contact Prayers (Salat); the Contact Prayers (Salat) are decreed for the believers at specific times.