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The correct answer is $-2$. It's given that a number $x$ is at most $17$ less than $5$ times the value of $y$, or $x\le 5y-17$. Substituting $3$ for $y$ in this inequality yields $x\le 5\left(3\right)-17$, or $x\le -2$. Thus, if the value of $y$ is $3$, the greatest possible value of $x$ is $-2$.