Besides the five prayers during the day and night times, there was another prayer which was obligatory for the Prophet (sws). It is called “the night prayer” or the tahajjud prayer. In the seventy ninth verse of Surah Bani Israil, this obligatory nature of the prayer for the Prophet (sws) is mentioned by the words نَافِلَةً لَكَ (https://www.javedahmedghamidi.org/#!/quran?chapter=17¶graph=25&type=Ghamidi). Then in Surah Muzzammil, it is further stated that when the Prophet (sws) was asked to deliver open warning to his people, he was specially directed to be diligent in this prayer. The Quran says:
يَاأَيُّهَا الْمُزَّمِّلُقُمْ اللَّيْلَ إِلَّا قَلِيلًانِصْفَهُ أَوْ انْقُصْ مِنْهُ قَلِيلًاأَوْ زِدْ عَلَيْهِ وَرَتِّلْ الْقُرْآنَ تَرْتِيلًاإِنَّا سَنُلْقِي عَلَيْكَ قَوْلًا ثَقِيلًاإِنَّ نَاشِئَةَ اللَّيْلِ هِيَ أَشَدُّ وَطْئًا وَأَقْوَمُ قِيلًاإِنَّ لَكَ فِي اَلنَّهَارِ سَبْحًا طَوِيلًاوَاذْكُرْ اسْمَ رَبِّكَ وَتَبَتَّلْ إِلَيْهِ تَبْتِيلًا
O you enfolded in your shawl! Stand [in prayer] by night, but not all night. Half the night, or even less or a little more and [in this prayer of yours] recite the Quran in a slow measured tone. Because soon We shall lay on you the burden of a heavy word. Indeed, this rising by night is very suitable for the mind’s peace and the heart’s resolve and for the speech’s correctness. Because during the daytime you will be hard-pressed with [this task; so pray at this time], and remember the name of your Lord, and [in this loneliness of the night] devote yourself entirely to Him. (73:1-8)
For common Muslims, this is an optional prayer and it is a great blessing for them if in following the Prophet (sws) they also offer this prayer. All the other prayers which the Prophet (SWS) had offered were not obligatory on Him (SWS) the way Tahajjud Prayer was made obligatory.