Find the largest value of $x$ that satisfies the equation $|x-5|=12$.
I notice that the equation involves the absolute value of $x-5$, which means that $x-5$ could be either positive or negative, but it must have a magnitude of 12. So I can rewrite the equation as two separate cases: either $x-5=12$ or $x-5=-12$. Solving for $x$ in each case, I get $x=17$ or $x=-7$. The question asks for the largest value of $x$, so I compare 17 and -7 and see that 17 is larger. Therefore, the largest value of $x$ that satisfies the equation is 17. 