**Puzzle:**

*Find the value of the question mark $\color{red}?$.*

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> $$(2, 13, 47)$$ $$(5, 7, 19)$$ $$(8, 1, \color{red}?)$$
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> **Hint 1:** $\color{red}?$ is a *prime*.
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> **Hint 2:** $\color{red}?$ is a *cyclops*.
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> **Hint 3:** $\color{red}?$ is a chain of *rings*. The middle one is black.
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> **Hint 4:** $\color{red}?$ is a *twin*.
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> **Hint 5:** The words *dialogue*, *education*, *housemaid*. What do they all have in common?
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I will not accept guessed answers.

Enjoy! :P

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**Edit:** The value has been found, as described in the answer below, but the pattern (or *main puzzle*, as the answer below has referred it to as) has not been solved just yet. Any thoughts? :)

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**Answer:**

Ok, nobody found the pattern of my puzzle and explained *why* $\color{red}?
 = 5$ and thus I will reveal to you the pattern. $\downarrow\downarrow\downarrow$

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>  $$\begin{align} 2(4+2) + 13^3 &= 47^2 \\ 2(4+5) + 7^3 &= 19^2 \\ 2(4+8)+1^3 &= \color{red}5^2.\end{align}$$
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I could have done something like

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>  $6(0+2)$, $6(1+2)$ and $6(2+2)$ because now we can replace $\{2, 5, 8\}$ with $\{0,1,2\}$, but I figured the former set would make the puzzle slightly harder :)
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I hope you enjoyed! :D