The evidence that it is obligatory is found in the Book of Allah, the sunnah of the Messenger of Allah, may Allah’s peace and blessings be upon him, and the definitive consensus of the Muslims—a matter necessarily known to be part of the religion.
As for the Book, Allah Most High says:
“Prayer is prescribed for the believers at specific times.” [Quran 4:103]
The point of evidence is His saying, “prescribed,” for this means something decreed, and what is decreed is obligatory. Allah Most High says:
“You who believe, fasting is prescribed for you…” [Quran 2:183]
That is, it has been made obligatory.
From the sunnah is the statement of the Prophet, may Allah’s peace and blessings be upon him, when he sent Mu'adh to Yemen: “Inform them that Allah has made five prayers obligatory upon them in every day and night.” (1)
As for consensus, it is necessarily known to be part of the religion. Therefore, none of those who profess Islam has denied its obligatory nature; even the adherents of religious innovation acknowledge that it is obligatory.
Upon every Muslim …
His statement, “upon every Muslim”: a Muslim is one who testifies that there is no god worthy of worship but Allah and that Muhammad is the Messenger of Allah; establishes the prayer; gives zakah; fasts Ramadan; and performs pilgrimage to the House.