Puzzle:
Find the value of the question mark $\color{red}?$.
$$(2, 13, 47)$$ $$(5, 7, 19)$$ $$(8, 1, \color{red}?)$$
Hint 1: $\color{red}?$ is a prime.
Hint 2: $\color{red}?$ is a cyclops.
Hint 3: $\color{red}?$ is a chain of rings. The middle one is black.
Hint 4: $\color{red}?$ is a twin.
Hint 5: The words dialogue, education, housemaid. What do they all have in common?
I will not accept guessed answers.
Enjoy! :P
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? :)
Answer:
Ok, nobody found the pattern of my puzzle and explained why $\color{red}? = 5$ and thus I will reveal to you the pattern. $\downarrow\downarrow\downarrow$
$$\begin{align} 2(4+2) + 13^3 &= 47^2 \\ 2(4+5) + 7^3 &= 19^2 \\ 2(4+8)+1^3 &= \color{red}5^2.\end{align}$$
I could have done something like
$6(0+2)$, $6(1+2)$ 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 :)
I hope you enjoyed! :D