5. Let $S$ denote the set of all positive integers whose prime factors are elements of \{2,3,5,7,11\}. (We include 1 in the set $S$.) If
\[
\sum_{q \in S} \frac{\varphi(q)}{q^{2}}
\]
can be written as \(\frac{a}{b}\) for relatively prime positive integers \(a\) and \(b\), find \(a+b\). (Here \(\varphi\) denotes Euler's totient function.)

Let's think step by step and output the final answer within \boxed{}.
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