The only explicit statement I found is
And I did not create the Jinn and mankind except to worship Me (51:56-58)
Are there any other explicit statements about the purpose of life in the Quran?
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There are a lot of places in the Quran that talk about the purpose of life. Here are two:-
قُلْنَا اهْبِطُوا مِنْهَا جَمِيعًا ۖ فَإِمَّا يَأْتِيَنَّكُم مِّنِّي هُدًى فَمَن تَبِعَ هُدَايَ فَلَا خَوْفٌ عَلَيْهِمْ وَلَا هُمْ يَحْزَنُونَ - 2:38
We said, "Go down from it, all of you. And when guidance comes to you from Me, whoever follows My guidance - there will be no fear concerning them, nor will they grieve.
This was said to Adam (AS) and by extension to all of humanity, where our purpose is to take and follow Allah's guidance (which is following the Quran and his final Prophet SAW).
الَّذِي خَلَقَ الْمَوْتَ وَالْحَيَاةَ لِيَبْلُوَكُمْ أَيُّكُمْ أَحْسَنُ عَمَلًا ۚ وَهُوَ الْعَزِيزُ الْغَفُورُ - 67:2
[He] who created death and life to test you [as to] which of you is best in deed - and He is the Exalted in Might, the Forgiving -
This is telling us our primary purpose of life which is for us to do as much good as we can.