To optimize this you have to invest your mathematical knowledge.
You should start from calculating prime using Sieve of Eratosthenes or some better algorithm.
Then note that all your q but first must be odd. All primes except 2 are odd and all their multiplication is odd too. As a result only first item in q is even.
Why this is important? Your sum has even number of elements, so to be able to have odd outcome which could match E in q, A must be equal to first element of q since it only even value in q.
So you have only 3 free parameters: B, C and D and E can be calculated and check if it exists.
You can iterate over B, C, D and then binary search for E in q. This will gives algorithm with complexity O(n^3 log n) which is great comparing to your O(n^5).
You can use unordered_set to match E in O(1) time instead of O(log n) time. So final algorithm easily ca be O(n^3).
I’m quite sure you can find this kind tricks more effectively. Possibly knowledge of d value could be used in some way to avoid some iterations.
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