Huge powers

First two consecutive prime numbers greater than \(10^7\) are \(p_{1} = 10000019\) and \(p_{2} = 10000079\) respectively. Let \(p\) be the smallest prime factor of \(S = p_{1}^2 + p_{2}^2-5\). Also, let \(q\) be the units digit of \(S\). What is the value of \(p+q\)?

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