Let's prepare for RMO #3

Find all the ordered pars of primes \(p,q\) such that \(\dfrac{(5^{p}-2^{p})(5^{q}-2^{q})}{pq}\) is an integer.

Submit your answer as sum of all \((p,q)\).


Note: \(p\) and \(q\) doesn't need to be necessarily distinct.

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