Are the five daily prayers mentioned in the Quran?

In the Tafseer of this aayah, it is reported that Ibn ‘Abbaas (may Allah be pleased with him) said: “The five daily prayers are (mentioned) in the Quran.” He was asked, “Where?” He said, “Allah says (interpretation of the meaning): ‘So glorify Allah when you come up to the evening’ is maghrib and ‘isha’; ‘and when you enter the morning’ is fajr; ‘in the afternoon’ is ‘asr; and ‘the time when the day begins to decline’ is zuhr.” Other mufassireen, such as al-Dahhaak and Sa’eed ibn Jubayr said the same thing. 

Some of the mufassireen said that these aayat mention only four of the prayers; ‘isha’ is not mentioned here, but it is mentioned in Soorat Hood, where Allah says (interpretation of the meaning): “… and in some hours of the night…” [Hood 11:114] 

Most of the mufassireen are of the first opinion. Al-Nahhaas (may Allah have mercy on him) said: “The scholars of Tafseer say that the aayah (interpretation of the meaning): ‘So glorify Allah when you come up to the evening and when you enter the morning…’ [al-Room 30:17] refers to the prayers.” 

Imaam al-Jassaas (may Allah have mercy on him) said: “Allah says (interpretation of the meaning): ‘… The prayer is enjoined on the believers at fixed times [mawqootan].’ [al-Nisa’ 4:103]. It was reported that ‘Abd-Allah ibn Mas’ood said: ‘[Mawqootan means that] Salaah has an appointed time just as Hajj does.’ It was reported that Ibn ‘Abbaas, Mujaahid and ‘Atiyyah said [that mawqootan means] ‘It is obligatory’… The word ‘mawqootan’ means that it is obligatory at certain times. The times are referred to in general terms in this aayah and are explained elsewhere in the Book, without defining precisely when those times start and end – that was explained in detail by the Messenger of Allah (peace and blessings of Allah be upon him).  What Allah mentioned about the times of the prayers in His Book is (interpretation of the meaning): “Perform al-Salaah from mid-day till the darkness of the night and recite the Quran in the early dawn…” [al-Isra’ 17:78]. Mujaahid reported from Ibn ‘Abbaas: “’Mid-day’ means when the sun has passed its zenith for salaat al-zuhr, and ‘the darkness of the night’ means the beginning of the night, for salaat al-maghrib.” It was also reported from Ibn ‘Umar that mid-day meant the zenith…  Allah says (interpretation of the meaning): “And perform al-salaah at the two ends of the day and in some parts of the night” [Hood 11:114]. ‘Amr reported from al-Hasan that ‘the two ends of the day’ means fajr at the first end and zuhr and ‘asr at the other; ‘some parts of the night’ means maghrib and ‘isha’. So according to this opinion the aayah refers to all five prayers….  Layth reported from al-Hakam from Abu ‘Ayyaad that Ibn ‘Abbaas said: “This aayah mentions all five prayers together. ‘So glorify Allah when you come up to the evening’ refers to maghrib and ‘isha’, ‘and when you enter the morning’ refers to fajr, ‘in the afternoon’ is ‘asr; and ‘the time when the day begins to decline’ is zuhr.” Something similar was also reported from al-Hasan. 

Abu Razeen reported from Ibn ‘Abbaas: “ ‘…and glorify the praises of your Lord before the rising of the sun and before (its) setting’ [Qaaf 50:39 – interpretation of the meaning] refers to the prescribed prayers. ‘… and glorify the praises of your Lord before the rising of the sun, and before its setting, and during some of the hours of the night, and at the sides of the day, that you may become pleased with the reward which Allah shall give you.’ [Ta-Ha 20:130 – interpretation of the meaning] This aayah also includes the times of the prayers. All of these aayaat mention the times of the prayers.” 

Ahkaam al-Quran by al-Jassaas, Baab Mawaaqeet al-Salaah. 

What you should also know is that the Quran does not contain details of all the rules. The Quran mentions many rules, but it also tells us that the Sunnah is a source of evidence in which many rules are mentioned in detail that are not mentioned in the Quran. Allah says (interpretation of the meanings):

“… and We have also sent down to you (O Muhammad) the reminder and the advice (the Quran), that you may explain clearly to men what is sent down to them and that they may give thought.” [al-Nahl 16:44]

“… and whatsoever the Messenger gives you, take it…” [al-Hashr 59:7]

The Prophet (peace and blessings of Allah be upon him) said: “I have been given the Quran and something like it with it…” (Reported by Imaam Ahmad, 16546; this is a saheeh hadeeth). Whether the rules were narrated in the Quran or in the Sunnah, all of it is true and right, and all of it has one source, which is the wahy or revelation from the Lord of the Worlds.