At the time of the Messenger of Allah (saws), there were five prayers prayed in the Mosque at five different times. The Quranic aayats regarding the timing of prayers are as follows:
Chapter 11, Surah Hud ayaat 114: Establish the Salat at the two ends of the day and in the early part of the night. (implies fajr, magrib and isha)
Chapter 2, Surah Baqarah ayaat 238: Take great care of your Prayers, especially of the middle Prayer and stand before Allah like devoted servants. (implies asr)
Chapter 17 Bani Israel ayaat 78: Establish the Salat from the declining of the sun to the darkness of the night and be particular about the recital of the Quran at dawn for the recital of the Quran at dawn is witnessed. (implies asr, magrib and fajr)
Chapter 30 Surah Rum ayat 17-18: So, glorify Allah in the evening and in the morning; praise is due to Him alone in the heavens and the earth: and (glorify Him) in the afternoon and at the declining of the day. (implies fajr, magrib, dhuhr and asr)
Chapter 50 Surah Qaf ayat 39-40: Therefore, O Prophet (saws), bear with patience whatever they say, and keep up glorifying your Lord with his praise, before sunrise and before sunset. And glorify Him again in the night and also when are free from prostrations. (implies fajr, dhuhr, asr, isha and tahajjud)
The prayer timings in the Quran are implied and thus if the above ayaats are read together, they clearly point towards the 5 obligatory fard prayers. A point to note when reading and understanding the Quran is that we must see how the Prophet (saws) understood and implemented the aayaats. The Prophet (saws) and all his companions prayed 5 times. Prayer was such a thing that it happened 5 times a day in front of thousands of people and thousands of people witnessed the timings and related them in their narrations. In times of extreme rain and travel, the Prophet (saws) did join sometimes the dhuhr/asr and also the magrib/isha prayers according to one tradition, but on a regular basis, he always led the congregation on the allotted 5 different times.Five times Prayer in Qur'an