The problem asks to write an inequality that represents the phrase "the quotient of $x$ and $3$ is less than or equal to $5$".

1. Problem Description

The problem asks to write an inequality that represents the phrase "the quotient of $x$ and $3$ is less than or equal to $5$".

2. Solution Steps

The quotient of $x$ and $3$ can be written as $\frac{x}{3}$ or $x/3$.

The phrase "less than or equal to" is represented by the inequality symbol $\leq$.

Therefore, the phrase "the quotient of $x$ and $3$ is less than or equal to $5$" can be written as $\frac{x}{3} \leq 5$.

3. Final Answer

$\frac{x}{3} \leq 5$