Shaykh Saalih Ibn Ghaanim as-Sadlaan رحمه الله said,
"It is clear that the obligatory nature of the obligatory prayers is established via the Book, the Sunnah and consensus.
As for the Book, the verses concerning it are many; these include Allaah's saying سبحانه و تعالى,
'And they have been ordered only to worship Allaah sincerely, making the religion for Him and to establish the prayer and give the Zakaah. That is the upright religion.' (Sooratul-Bayyinah, 98:5)
As for the Sunnah, there are also many ahaadeeth concerning this. For example, Imaam al-Bukhaaree رحمه الله, Imaam Muslim رحمه الله and others report from 'Abdullaah ibn 'Umar ibn al-Khattaab رضي الله عنهما that he heard the Messenger of Allaah صلى الله عليه وسلم saying,
بُنِيَ الْإِسْلَامُ عَلَى خَمْسٍ: شَهَادَةِ أَنْ لَا إلَهَ إلَّا اللَّهُ وَأَنَّ مُحَمَّدًا رَسُولُ اللَّهِ، وَإِقَامِ الصَّلَاةِ، وَإِيتَاءِ الزَّكَاةِ، وَحَجِّ الْبَيْتِ، وَصَوْمِ رَمَضَانَ
'Islaam is built upon five pillars: the testimony that none has the right to be worshipped save Allaah and that Muhammad is the Messenger of Allaah, establishing the prayer, giving the Zakaah, performing Hajj and fasting the month of Ramadaan.' 
As for the consensus, Imaam Ibn Hubairah رحمه الله said in al-Ifsaah, 'They [the scholars] have unanimously agreed that the prayer is one of the pillars of Islaam and that there are five obligatory prayers during the day and night... They have also agreed that the obligation is never lifted with regards to the legally responsible, mature, sane men. They have been enjoined with it until the time of their death or the commencement of the matters of the Hereafter.'"  
 Reported by al-Bukhaaree [Eng. Trans. 1/17 no. 7] and Muslim [Eng. Trans. 1/9 no. 18-21].
 al-Ifsaah 'an Ma'aanee as-Sihaah (1/100) of Imaam Ibn Hubairah al-Hanbalee رحمه الله.
 Shaykh Saalih Ibn Ghaanim as-Sadlaan رحمه الله, Congregational Prayer (Al-Basheer Publications & Translations), p. 17.